Strange But Charming: 2023

Nielsen-Ninomiya No-go Theorem

An interesting paper which I have been fascinated by recently is the paper by Holger Nielsen and Masao Ninomiya, which shows that there exists a no-go theorem concerning fermion doubling with chiral fermions on a lattice. Naively, the idea is that the Hamiltonian for fermion field has fermion doubling if the following conditions are satisfied: (1) translational invariance is satisfied, (2) the charges are conserved and quantized, and (3) the interaction Hamiltonian is Hermitian and local. In this sense, there is a no-go theorem, the original arguments of which concern homotopy theory. There is also a very good paper by Friedan on a proof of this theorem. There were some arguments concerning if one could be a little more lenient with the hermiticity condition, and impose something like the PT symmetry, see for instance The Nielsen-Ninomiya theorem, PT-invariant non-Hermiticity and single 8-shaped Dirac cone. There is also a very good paper on the approach from loop quantum gravity by Jake Barnett and Lee Smolin, which seems to have some interesting features. Seemingly, there seems to be emphasis on circumventing the Nielsen-Ninomiya theorem in LQG, which seems to be an interesting remark. A part of the theorem's popularity also lies with the motivation it provides to other things with fermions, most famously massive fermions, which is something that David Tong has worked on.

Holography and Theory Journal Club

We're launching a journal club, for which I am the organizer, called Holography and Theory Journal Club, where we will have weekly or bi-weekly (i.e. every other week) discussion meetings or invited talks on recent works in hep-th. We accept the submission of meeting abstracts, for which a forms link is provided in the website, https://sites.google.com/view/htjc. Kindly note that all talks will be by invitation only, whereas paper discussion meeting abstracts are welcome unsolicited. Preferably, the papers are from the hep-th arXiv in the week of submission itself, so that there are no misses of important papers. We will also have a mailing list ready this by Monday, so just drop in an email for participating in the journal club till then!

P.S. Working on a set of notes on Ricci flows in Kahler manifolds.

Black Hole Information Paradox Notes

Notes on the black hole information problem, which I wrote in a very elementary fashion have been complete. I must say that a part of my inspiration to write this was from Aayush's notes, and I wanted to add on to the discussion in a slightly more elaborate way. Keep in mind that this is not a very AdS/CFT oriented thing, so it may seem to be off-topic for the title. However, in the next set of notes, I talk about the Almheiri, Engelhardt, Marolf and Maxfield + Pennington works exclusively. This series of notes, Bulk Physics, Algebras and All That was originally a three-part series. Now, it is an $N$-part series in the large $N$ limit.

Bulk Physics, Algebras and All That -- Part Two: Black Hole Information Problem

Black Hole Interior in AdS/CFT

Black holes in AdS/CFT are interesting things. One could ask if, following along with the usual bulk-boundary description, there is a way to find CFT operators dual to bulk fields in the exterior and interior of a large AdS-Schwarzschild black hole. The exterior is simple enough; it is our usual HKLL scheme that has to be used. This is following the extrapolate dictionary,

\[\mathcal{O}(t, \Omega )=\lim _{r\to \infty }r^{\Delta }\phi (r, t, \Omega )\;,\]

where $\Delta $ is the usual conformal weight. One could also sit in the Poincare setting for working with the expansion of these operators and modes. The primary idea here is that dual to a bulk field, one can either take a set of local operators that are ``smeared", or a family of nonlocal operators instead. For instance, solving $(\Box -m^{2})\phi =0$, and compressing each set of Bessel functions and denoting the normalizable mode by $\xi _{\omega , k}(t, x, z)$ as in 1211.6767, a nonlocal CFT operator in the Poincare patch looks like

\[\Phi _{\text{CFT}}(t, x, z)=\int \frac{d\omega d^{D-1}k}{(2\pi )^{D}}\;\mathcal{O}_{\omega , k}\xi _{\omega , k}(t, x, z)+\mathcal{O}^{\dagger }\xi ^{*}_{\omega , k}(t, x, z)\;.\]

Then, operators in region II of the Penrose diagram can be written as

\[\phi ^{\text{II}}_{\text{CFT}}(t, x, z)=\int _{\omega >0}\frac{d\omega d^{D-1}k}{(2\pi )^{D}}\; \mathcal{O}_{\omega , k}g^{(1)}_{\omega , k}(t, x, z)+\tilde{\mathcal{O}}_{\omega , k}g^{(2)}_{\omega , k}(t, x, z)+\dots \;.\]

This is obtained from interpolation between operators in the regions I and III. Read more on this in 1211.6767 and 1310.6334. More on this will be detailed in Part Two of my Bulk Physics, Algebras and All That notes, which will come out by tomorrow.

Where is High Energy Physics Going?

I came across this Phys.SE post, to which there is a particular answer that states the following, quoted:

``... but can tell you this. High Energy Physics goes nowhere now as String Theory fails to produce any measurable prediction in two decades. There is no progress in standard model too. Problems left in GR/math ph. are either very difficult or exotic. If I were you I'd choose a field as close to experiment as possible because standard theoretical physics is practically dead. "

My first reaction is best described by three letters: lol. However, I thought I would expand a little more on this, while listening to Style by Taylor Swift.

The statement that hep-th goes nowhere as far as string theory is concerned because it ``fails to produce any measurable prediction in two decades" is an absurd one. While I am not a string theorist, there have been plenty of developments as far as theoretical hep is concerned. If you want a debatable and non-trivial problem to work on, go for string theory and de Sitter space. Putting aside the part that there ``is no progress in standard model" (since I am not aware of it), there is the next statement that ``problems left in GR/math-ph are either very difficult of exotic". Putting aside that most of the problems in pure GR right now are either things appealing to math.DG or math.AP, or things requiring numerical brute-force computations (see the state of the gr-qc arXiv), I doubt there are many problems in the overlap of gr-qc and hep-th that are ``exotic", defined by the poster as meaning ``... of little importance to physics".

The second aspect of this is that in the face of modern hep-th, math-ph is a very hot topic. At any given time, the math-ph arXiv has at least two papers whose primary listing is hep-th. And for that matter, string theory in the mathematical physics arXiv is very infamous, owing to the fact that most of string theory appeals to a wide range to things like math.RT, math.QA, math.NT and math.DG to name a few. Hep-th does not simply mean the surface level works with AdS/CFT or so, and is a field that has very beautiful things to work with. And finally, as of ``... choose a field as close to experiment ... theoretical physics is practically dead", one may see the hep-th arXiv instead to get a better understanding of how very much alive theoretical physics is. From my side, there are some topics that I would provide as examples:

JT gravity. For instance, today a paper appeared which works with the semiclassical Bousso bound in JT gravity. It has also worked alongside random matrix theory.
Operator algebras. In all sorts of places, most strikingly in AdS/CFT.
Information theoretic aspects with things like pseudo Renyi entropy and non-trivialization of Araki's definition of relative entropy for density matrices into complex valued entanglement entropy.
de Sitter space. For instance, Chandrasekharan, Longo, Pennington and Witten recently worked on static patch algebra of observables and type II$_{1}$ algebras.
Information problem and islands.
Topological QFTs.
Involvements of math.AG (see for instance Kapustin and Witten's paper on the electromagnetic duality and geometric Langlands).

Naval Footage

I found some amazing videos of WW2 footage. Some are remastered and edited, but they are worth watching. Music is kind of annoying.

The Definition of a CFT

Here is the second part in Segal's track titled The Definition of a Conformal Field Theory. Puts things in a nice mathematical perspective that the usual introduction to CFTs does not offer. Besides this there is the Langlands mix of CFTs by Frenkel, but I cannot recommend it to anyone who (like me) are not well established with it.

The Definition of a Conformal Field Theory -- Graeme Segal

Travel Reading!

I am going to be travelling for about two days, and I am not a fan of travelling. But a good thing is that I can take a break from working and instead read a few papers. So here are a few papers that I am sharing for you to also have some nice reading time ;) No specific theme, but a collection of things I want to read. Happy reading.

Algebraic ER=EPR

A paper I have been looking forward to with a lot of excitement since Netta's Strings talk has finally been arXived. It was worked on in conjunction with Hong Liu, who previously worked on algebra in AdS/CFT with Samuel Leutheusser in their subregion-subalgebra and emergent times papers. I had written a bit on algebraic ER=EPR in my notes on bulk reconstruction and subregion duality, where I briefly discussed this based on her Strings talk slides.

[2311.04281] Algebraic ER=EPR and Complexity Transfer

Interestingly, the way I had tried to make an algebraic formulation of a ``strong" No Transmission Principle had a lot to do with the identification of type I and type III algebras. I may not arXiv that draft, but for the sake of it I may archive them here soon. For instance, in the paper by Engelhardt and Liu, the type I statement is that taking the bulk Hilbert space $\mathcal{H}_{bulk}=\mathcal{H}^{Fock}_{R}\otimes \mathcal{H}^{Fock}_{L}$, the boundary algebras $\mathcal{A}_{R}$ and $\mathcal{A}_{L}$ are type I if they are disconnected -- if they are connected, it must be type III (classically connected, or type II if quantum connected). The idea I had was that of a strong NTP, so that if the algebras are type I the bulk duals must be ``independent". The statement of the strong NTP was meant to be a strengthened version of NTP, saying that if the boundary CFTs are type I, they are disconnected and the bulk duals being disconnected should imply that the Cauchy slices are incomplete. I was yet to make this more precise when I saw Engelhardt's Strings talk.

Homotopy et TQFTs

The essential idea of TQFTs is that they are a symmetric monoidal functor $\mathcal{Z}$ from the category of topological spaces, here $n$-bordisms (with a number of technicalities suppressed for now):

\[\mathcal{Z}\;:\; \text{Bord}_{n}\;\longrightarrow \;\text{Vect}_{\mathbb{K}}\;.\]

$\mathcal{Z}$ is functorial w.r.t orientation preserving diffeomorphisms of $\Sigma $, an oriented smooth $D$-manifold and $M$, a $D+1$ manifold. The general approach is by defining a homotopy axiom and an additive axiom, in the sense that one can attribute the above functorial definition. In the TQFTs the homotopy axiom, which has to do with cylinders, is replaced by cobordisms instead -- established by Atiyah in his paper on topological quantum field theories. One can now use this as a starting point and define homotopy quantum field theories (HQFTs) as the following alteration of the above definition: taking $\mathbf{B}$-cobordisms, one can define the symmetric monoidal category $\textbf{Hcobord}(n, \mathbf{B})$. Then, an HQFT is a functor:

\[\mathcal{Z}^{\mathcal{H}}\;:\;\textbf{Hcobord}(n, \textbf{B})\; \longrightarrow \;\text{Vect}_{\mathbb{K}}\;.\]

There are some more aspects about $\text{Vect}_{\mathbb{K}}$ that are of importance, but I do not have an understanding strong enough to explain them.

Nonlinear PDE aspects of Ricci Flow

While in discussion with a colleague, I remembered Terry Tao's excellent paper on the nonlinear PDE aspects of Ricci flow and the Poincare conjecture. See Perelman's proof of the Poincaré conjecture: a nonlinear PDE perspective. See also his slides on the Poincare conjecture proof: Perelman's proof of the Poincaré conjecture. I personally am fascinated by the Sacks-Uhlenbeck theorem, which has to do with a nontrivial $\pi _{2}(M)$ and shows the finite-time existence of singularities. This finds its way in turn into what Hamilton first showed as a kind of finite-time existence of singularities. It is also interesting how the homotopy cobordism theorem aspects also have implications in a fundamental sense.

H-cobordisms, Manifolds and Poincare

The h-cobordism theorem is essentially the following result: Let $M$ be a simply connected $N-$cobordism (with $N\geq 6$) between $V_{0}^{N-1}$ and $V_{1}^{N-1}$. Then, $M\xrightarrow{\;\cong\;}V_{0}^{N-1}\times [0, 1]$. Then, if $M$ is a contractible manifold, one has $M\xrightarrow{\;\cong\;}\mathbb{D}^{N}$. We can prove this as follows: Let $\mathfrak{G}$ be an embedding of $\mathbb{D}^{N}$ into $M$ and identify the interior $\mathrm{Int}(\mathbb{D})$, for which $M-\mathfrak{G}\left(\mathrm{Int}(\mathbb{D}) \right)$ is a cobordism $\partial M\Longleftrightarrow \mathbb{S}^{N-1}$. If we piece these sections back, we would have $M$ from $\mathbb{D}^{N-1}$ and the cobordism $M-\mathfrak{G}\left(\mathrm{Int}\left(\mathbb{D} \right) \right)\equiv \mathcal{B}$. The following pushout diagram shows this decomposition:

Here, $\mathcal{B}$ is simply connected (due to homotopy cofiber sequence $\mathbb{S}^{N-1}\to \mathcal{B}\to M$), and therefore, one can has $\mathbb{S}^{N-1}\xrightarrow{\;H\cong\;}\mathcal{B}$, where $A\xrightarrow{\;H\cong\;}B$ denotes homotopic equivalence. Now, one can use the h-cobordism result from theorem to identify that $\mathcal{B}\xrightarrow{\;\cong\;} \mathbb{S}^{N-1}\times [0, 1]$. Gluing $\partial \mathbb{D}$ back, one sees that $M\xrightarrow{\;\cong\;}\mathbb{D}^{N-1}$, completing the proof. Then, we note the follows: Given a map $\mathfrak{G}$ between $\mathbb{S}^{N-1}$, one can identify that there exists a homeomorphism $\mathfrak{F}$ between $\mathbb{D}^{N}$:

Then, the Poincare conjecture can be rewritten into the follows: An $N-$manifold that is homotopy equivalent to the $\mathbb{S}^{N}$ is also homeomorphic to $\mathbb{S}^{N}$. As you can guess at this point, the proof of this is somewhat straightforward in terms of the decomposition of the primes $\mathbb{D}^{N}_{\pm }$ and $\mathbb{S}^{N-1}_{\pm }$ under the assumption of the h-cobordism theorem. The proof is as follows. The first diagram shows the decomposition of $M=\mathbb{D}_{0}^{N}\sqcup \mathcal{B}\sqcup \mathbb{D}_{1}^{N}$ by identifying the boundaries of the disks and $M-\mathfrak{G}\left(\mathrm{Int}\left(\mathbb{D}_{0}^{N}\sqcup \mathbb{D}_{1}^{N} \right) \right)\equiv \mathcal{B}$. Next, using the Alexandrov trick to induce $\mathfrak{F}$ on $\mathbb{D}^{N}$ from $\mathfrak{G}$ homeomorphism induced on $\mathbb{S}$, we would get the second diagram below:

From the second diagram where we used the Alexandrov trick, we see that there is a homeomorphism between $\mathbb{S}^{N}$ and $M$ by identifying the maps of the $N-$disks. However, in using the h-cobordism theorem, one has to be sure that the inclusion maps \textit{indeed} have the homotopy equivalence nature. This can be found as a lemma:

Lemma: If $M$ is homotpic to $\mathbb{S}^{N}$ and $\mathcal{B}$ is a cobordism between $\mathbb{S}_{0}^{N-1}$ and $\mathbb{S}_{1}^{N-1}$ as obtained from the subtraction of the $N-$disk images $M-\mathfrak{G}\left(\mathrm{Int}\left(\mathbb{D}_{0}^{N}\sqcup \mathbb{D}_{1}^{N} \right) \right)$, then $\mathbb{S}_{0}^{N-1}\hookrightarrow \mathcal{B}$ is a homotopy equivalence.

Due to the above lemma, one can use the h-cobordism theorem to show that there is a homeomorphism between $\mathbb{S}^{N}$ and $M$, concluding our proof. This proof works (with several subtleties) in $N\geq 6$. This discussion is taken from my notes. However, the Ricci flow approach is much more interesting, since it has a lot to do with the finite-time existence of singularities. Based on the nature of prime decomposition, the works of Hamilton and others, and most importantly Perelman, showed that one can do surgery and continue Ricci flow. To illustrate this, consider the neckpinch characterized by the nature of a pullback being a shrinking cylinder soliton. To prove Poincare from Ricci flow, one has to show the finite time existence of the connected sum decomposition, which forms the basis of Perelman's work.

Bulk Physics, Algebras and All That: Part One

A set of notes, titled Bulk Physics, Algebras and All That, which I have been writing from a couple of weeks has been almost completed. This set of notes is split into three parts -- part one, where bulk reconstruction and aspects of subregion duality are discussed; part two, where most of the focus is on QES and things like their relation to the information problem in AdS/CFT is presented; and part three, where some of the recent things I learnt about JT gravity and SYK model are discussed. Part three still needs some work, but as of now part one has been completed. There are some omissions and refinements to take into account in future revisions, due to which for now, here is part one.

Bulk Physics, Algebras and All That -- Part One: Bulk Reconstruction and Subregions

Review paper on de Sitter and Holography

A review paper on de Sitter and holography that I have been collaborating on with Aayush Verma has been completed. While this is a preliminary version and we may not arXiv it immediately (perhaps after some more refinements), the present state of the paper justifies to an extent the title. It is based on discussions on the general aspects of de Sitter, holographic entanglement entropy from usual dS/CFT and bit threads, the recent works by Suvrat et al on the Hilbert space of de Sitter quantum gravity, the work on algebra of observables in de Sitter space by Chandrasekharan, Longo, Pennington and Witten, some brief aspects of Cauchy slice holography by Wall et al, and finally a mention of bulk reconstruction in the sense of dS/CFT. In upcoming revisions, we will elaborate on some aspects and include further works, such as cosmic ER=EPR by Cotler and Strominger, dS/dS, and Balasubramaniam et al's works on de Sitter space.

Revering Musings on de Sitter and Holography

U-boats

The history of naval warfare is perhaps one of the most intriguing things, and I am not hesitant to admit that I am obsessed with reading about these things. And one cannot talk about naval warfare and not talk about U-boats (or U-boots as they were called in the Kriegsmarine). So this post is to share a bit on the effectiveness of U-boats.

Keep in mind that after WW1 Germany was forced to minimize military forces under the Treaty of Versailles. And then Hitler came along, and here Germany saw a massive expansion in the armed forces, particularly interestingly, the Luftwaffe and the Kriegsmarine. The latter developed powerful dreadnoughts like the Bismarck (lost tied to Operation Rheinubung, which also involved Prinz Eugen), Tripitz, Lutzow, and many others. But the particularly interesting class of developments were in the family of U-boats, which had two essential armaments -- a deck gun, which I think was usually an 8.8 SK/C-35, and around 14 torpedos. To quote Winston Churchill is to best describe how effective these were in raiding shipping lanes in Wolfpack operations: ``the only thing that really frightened me during the [second world] war was the U-boats peril". Eventually, of course, the effectiveness declined because of anti-submarine warfare (ASW) like Hedgehog (which had bow-forward throwing mortars), Depth charges (these were usually the more effective ones, more below) and the Leigh light among others. One more thing that happened in this period was the cracking of the Enigma from U-boat wrecks, which was a major turning point in the war.

From a purely psychological perspective, there were a number of pressures on U-boat crews. More often than not, they would be subject to hours of constant depth charging, which was a technique that turned out to be quite effective. This was because the Depth charges, thrown to the stern-backward would not have to necessarily impact the U-boat, or even detonate anywhere close to it; it only sufficed to explode in a certain radius for the U-boat to have significant damage, usually damaging ballasts, steering, sonar or the entire U-boat altogether. And since U-boats had to recharge batteries, they would have to surface, which they usually did at night in the early war periods. However, after aerial spotting and bombings of U-boats became superior, this was pushed to the day time. Before the Allies developed an effective countermeasure to U-boats (which initially did not work so well), U-boat campaigns were very successful. They referred to the time period around July, 1940 as the First Happy Time, or Die Gluckliche Zeit. There is a Second Happy Time as well, however I won't discuss this.

For that matter, U-boats in WW1 were also recognized as a threat -- however, they did not operate at the scale seen in WW2. The sinking of Lusitania and the Arabic significantly increased pressure on the American-German relations, and at that point the predictability of a move from Britain was not unseen. In the August of 1915, the Baralong incidents took place, which in a single line can be summarized by ``... [unofficially] ... take no prisoners from U-boats". While this was seen as a British war crime, many say that the provocation of the U-boats was not minor, since attacking Lusitania was in itself a crime, although the German claim was that this was justified since Lusitania could also be classified as an auxiliary cruiser. Joining the dots, it should be clear that there are many aspects of historic value involved when discussing just the one topic of U-boats. Of course, there are many other historically significant cases, like Battle of Jutland, Operation Rheinubung, and many others. In fact, the Battle of Jutland is one of three actions in a major war that involved battleships, after Battle of Yellow Sea and most notably, the Battle of Tsushima, which is famous for Admiral Togo's strategic ``U-turn", which crossed-the-T of Admiral Rozhestvensky's fleet. Tsushima is also famous for Admiral Togo's famous quote, ``Weather today fine, but high waves". However, more on these later.

Botez Gambit! And two new papers

I have been somewhat obsessed with chess recently, after successfully winning my tenth game day before yesterday. However, often unsuccessfully, I have found myself making the mistake of trying the Botez Gambit. However, I was successful in ensuring that every time my Queen was lost, the opponent's psychology would be at stake. Partly since the opponent may overestimate the value of the Queen in the particular scenario we would be in, due to which I would be able to either also take off the board the opponent's Queen, or ruin the endgame for the opponent altogether. I will add to this post some of my musings and a particularly interesting experience (so far) to this post once I get time. Also, on today's arXiv, we have the following two nice papers:

Thermal Bekenstein-Hawking entropy from the worldsheet

What if Quantum Gravity is "just'' Quantum Information Theory?

Holographic Entanglement Entropy without Holography

Today, in the morning, I was learning how to do the Botez Gambit without making it a fail, when (after failing to make good of it in the last 30 seconds) I opened arXiv and saw a paper by Marolf and collaborators. The paper has to do with the notion of Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi without AdS/CFT. While this particular title seems to not be very new (since bit threads are independent of holography up to a certain extent), the paper in itself is an amazing read, and unless Engelhardt and Liu's work on Algebraic ER=EPR comes out this month (which I hope it does), this would be the read of the month. Pasterski and collaborators also had a paper, but I am not into celestial holography, so I cannot say anything about it.

Algebras and Hilbert spaces from gravitational path integrals: Understanding Ryu-Takayanagi/HRT as entropy without invoking holography

Extremal surfaces in de Sitter

Today, a paper by K. Narayan came up on arXiv. However, I had the privilege of seeing the draft from two days earlier, and here is a quick glimpse on why these extremal surfaces are important. From AdS/CFT, we know that extremal surfaces are the things that make up the entanglement wedge, where we do all sorts of nice things like entanglement wedge reconstruction, make sense of subregion-subalgebra duality (at least motivationally) and calculate entanglement entropy, etc. One interesting thing is that of phase transitions, where if you vary the area of a two-component boundary subregion, the corresponding entanglement wedges eventually coincide, and you will be able to reconstruct a bulk operator deeper than before. But, such kinds of things only exist because these extremal surfaces have that interpretation. In dS/CFT, this becomes a very subtle question: if one does construct entanglement entropy (which we nicely can), what subreion duality could we possibly construct? Clearly this has to be Lorentzian, i.e. into the bulk from $\mathcal{I}^{+}$ to $\mathcal{I}^{-}$ (without ``turning points" going to the same boundary), due to which we have to make sense of extremal surfaces going timelike. This paper has a very nice description of the extremal surfaces, and I have some thoughts on a possible reconstruction scheme in this scenario. However, it must be noted that, while subregion duality has been previously highlighted in AdS/CFT with the backing of type III$_{1}$ von Neumann algebras associated to the bulk and boundary subregions, I am not sure about the nature of algebras in this case. So, things like JLMS and pure bulk reconstruction schemes do not exist as of yet. However, this is an interesting field, and I think the next big thing will be in dS/CFT.

Physicists Joking Around

A little strange for a post, but I found this interesting video on YouTube that I found nice. I found this after searching for ``physicist breaks down", which is a gag video from The Big Bang Theory show, where Sheldon drinks alcohol and jokes around. I have linked both the videos, in case you want to have some time off from work.

Theoretical Physicists having fun & cracking jokes

Physicist Melts Down (TBBT)

Paper by Flam, Leutheusser and Satischandran

A new paper had appeared yesterday by Flam, Leutheusser and Satischandran, called Generalized Black hole entropy is von Neumann Entropy. I have to read this, although I am having to go through Liu and Leutheusser's three previous works for my works.

Generalized Black Hole Entropy is von Neumann Entropy

Papers for beginners in AdS/CFT!

For people who are interested in what I am doing (in AdS, while dS has some other works as well), here are some papers that are worth referring to, since most of my works are based around these results. Mainly, the following are people whose works are extensively referred to: Raphael Bousso, Netta Engelhardt, Andy Strominger, Aron Wall, Tadashi Takayanagi, Veronika Hubeny, Mukund Rangamani, Shinsei Ryu, Geoff Pennington, Ahmed Almheiri, Juan Maldacena, Ed Witten, Thomas Faulkner, Aitor Lewkowycz, and Horacio Casini. Of course, there are many others, but in AdS/CFT, these are some of the key ones. Keep in mind that these are not in any chronology; I am working on a review, in which perhaps I will detail on this.

Holographic Derivation of Entanglement Entropy from AdS/CFT (Ryu-Takayanagi),

Coarse Graining Holographic Black Holes (Engelhardt, Wall),

Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime (Engelhardt, Wall),

Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy (Wall),

Relative entropy equals bulk relative entropy (JLMS),

Recovering the QNEC from the ANEC (Ceyhan, Faulkner),

Relative entropy and the Bekenstein bound (Casini),

Gravity Dual of Connes Cocycle Flow (Bousso, Chandrasekharan, Rath, Mogghadam),

Large and Small Corrections to the JLMS Formula from Replica WormholesFlam, Rath,

Large N algebras and generalized entropy (Chandrasekharan, Pennington, Witten),

Emergent times in holographic duality (Leutheusser, Liu),

Holograms In Our World (Bousso, Pennington),

Entanglement Wedges for Gravitating Regions (Bousso, Pennington),

Canonical Purification of Evaporating Black Holes (Engelhardt, Folkestad),

Local bulk operators in AdS/CFT: a boundary view of horizons and locality (HKLL),

And there are some other works too, but for now I think these are nice.

Modular flows, operators and AdS/CFT

See Weisbrock's paper on half-sided modular inclusions. This finds a very striking application in Ceyhan and Faulkner's paper on finding QNEC from ANEC, and in Bousso, Rath, Chandrasekharan and Mogghadam's work on the gravitational dual to the Connes cocycle flow. In AdS/CFT, this is very successful, and I think there are some other papers that use modular theory, and I will add some more papers soon.

Pseudo-Hermitian Quantum Mechanics

Lately, I have been caught up with some works requiring me to extensively think about the possibilities of un-Hermitian quantum mechanics. One of these was that the existence of higher spin theories as dS/CFT, initiated by Anninos and collaborators. While I am really naive about this, I think there could be motivations to pseudo-Hermitian quantum mechanics particularly in de Sitter, and with important implications to calculating entanglement entropy. While on this topic, Jacob Barnett arXived his thesis, entitled Locality and Exceptional Points in Pseudo-Hermitian Physics a while back. The appendix of this thesis discusses many elementary aspects of the mathematics involved in the thesis.

And on the topic of papers in dS, there is a nice paper today that I wish to read eventually: Unitary-Preserving Holography in dS$_d$ [2309.02122].

Complexity paper: Timelike separated QES

Netta Engelhardt, Geoff Pennington and Arvin Shahbazi-Mogghadam had a paper on arXiv two days ago (the most recent posting*) on quantum extremal surfaces and Python's lunch. Interestingly, it also describes a kind of quantum extremal surface that resembles a de Sitter bifurcation surface.

*Friday, 1st September, most recent since arXiv papers are not announced on weekends.

Twice Upon a Time: Timelike-Separated Quantum Extremal Surfaces [2308.16226]

Good Will Hunting

Just two clips from Good Will Hunting (1997). This happens to be my comfort movie, which I would recommend to anyone wanting to see a movie feel like a nice hug. Matt Damon and Robin Williams definitely made this movie one of (if not) the most perfect movie. It is with reason that I ranked this first on my movies page.

Perfect for Each Other: Sean (Robin Williams) telling Will (Matt Damon) about wife, and what made their relationship what it was -- the little things. One of the most heartfelt scenes I have seen in a movie. The camera shaking when Sean jokes about his wife, the suiting silence -- there are many things I can say just about this one scene.
It's Not Your Fault: Sean telling Will that his father causing his traumatic childhood is not something he has to reflect himself with. Again, one of the most heartfelt clips in a movie ever, particularly the almost child-like way Will holds Sean, who broke the emotional baggage that Will built up all his life.
Gotta Go See About a Girl: Sean talking about how he met his wife, missing the game, to which Will is perplexed.

Strings, strings and strings

Today, on Twitter I came across a post by Thomas Van Riet [see here], that seeing Strings 2023, the name of the conference should be ``the conference previously known as Strings". This is true -- in fact, so much so that Aron Wall at the beginning of his talk said something along the lines of ``... I am going to do something unusual, and actually talk about string theory ...". Of course -- string talks were present quite nicely; for instance, Remmen gave a talk on his work with Cheung on bespoke dual resonance [2308.03833], Wall on off shell strings and black hole entropy, Sen on logarithmic corrections to supersymmetric black holes and Eberhardt for instance. That said, there were a number of talks that weren't exactly strings -- for instance, Suvrat's talk on the Hilbert space of de Sitter quantum gravity, Engelhardt on an algebraic ER=EPR with Hong Liu (something I am excited to read on, since I had some speculation on similar lines), and Strominger on cosmic ER=EPR in dS/CFT with Cotler. For that matter, a stringy context of de Sitter is something I (and presumably some other people) are wary of. The most ``trustworthy" paper I have read on de Sitter compactifications in string theory is the one by Van Riet, Bena and Grana [2303.17680]. However, I think the star of the show (pardon me for this statement; I found many other talks great as well, but... Well..) was Witten's talk on a background independent formalism for quantum gravity, based on the paper [2308.03663].

But, unsurprisingly (since it is Twitter), some people pointed out some opposition to string theory. Well.. I suppose this is where I say that politics arises with trying to compete with string theory. Between Republicans and Democrats, I may be able to choose at some point given some understanding. But with string theory, I doubt anyone will ever say ``oh! Loops look better now!". Or indeed any other theory. Anyone saying ``that theory is wrong, this is better" are essentially trying to gamble with this false politics.

P.S. Twitter is messed up. Millions of years of evolution and this is what it boils down to.

Susskind's de Sitter papers and IAS talk

Only a few days ago, Susskind gave a talk called Observers and Observations in de Sitter space at IAS hep meetings. The following are some papers to read and some other talks to read in close reference to this.

While I am not aware of DSSYK$_{\infty }$, I think Susskind will give a talk soon at IAS (as mentioned to Witten at the end of the talk).

Bit Threads, AdS/CFT and de Sitter

Recently, I came across a very striking formulation of Ryu-Takayanagi's result in AdS/CFT due to Freedman and Headrick [1604.00354]. While I came across this from reading Frederick and Hubeny's paper on Covariant Bit Threads [2208.10507] (and also from Susskind and Shaghoulian's paper on de Sitter entanglement [2201.03603]), I felt that this proposal has some things to be understood even in the framework of AdS/CFT. The idea is summarised as follows: due to a max-flow-min-cut theorem for Riemannian manifolds, one can state the Ryu-Takayanagi area-minimizing term as a max-flow for bit threads.

Start from Ryu-Takayanagi (where $\sim $ denotes that the surface is homologous to the boundary subregion):

\[S(\partial R)=\max _{\Sigma }\min _{\mathcal{X}\sim \partial R} \text{Area of } \mathcal{X}\;.\]

Usually, the term $\max _{\Sigma }$ is redundant and is instead used in the HRT prescription for covariant holographic entanglement entropy. From the max-flow-min-cut principle, the term $\min _{\mathcal{X}\sim \partial R}$ can be replaced by maximizers of the flow $v$, which has field lines defined as bit threads. These have two properties: (1) they have a fixed ``width" of $1/4G_{N}$, and (2) they cannot cross a horizon. Ryu-Takayanagi then becomes

\[S(\partial R)=\max _{\# \text{ threads}} \int v\;,\]

where by maximizing flows $v$ we mean the number of threads that leave the boundary subregion. These bit threads have an additional property: they always start and end on the boundary. Ryu-Takayanagi then takes the above form, and is fully expressed in terms of the maximum $\#$ of bit threads leaving the subregion into the bulk, forming a ``bottleneck". This is preserved from the max-flow-min-cut theorem, and so the definition of Ryu-Takayanagi is still the same.

Susskind and Shaghoulian introduced this aspect of bit threads and entanglement entropy in de Sitter space, which is an interesting read. In de Sitter, one does not have this conformal boundary nature to describe a nice picture for entanglement entropy. Instead, as Susskind and Shaghoulian pointed out, one can define a Ryu-Takayanagi formula in static patch by identifying a surface between the stretched horizons to find the entanglement of the pode-antipode system. This reduces to the familiar Gibbons-Hawking entropy,

\[S=\frac{\text{Area of } H_{\Lambda }}{4G_{N}}\;.\]

In the bit threads formulation, one now has the ability to define two proposals: first, a monolayer proposal, where each horizon emits bit threads towards the other component in a single-layered fashion, and second, a bilayer proposal, where the largest component (usually the cosmic horizon) emits bit threads in a double-layered fashion. Due to this, one has bit threads going (1) to the other component, and (2) ``backwards" towards the pode or antipode. Of course, these bit threads find a bottleneck of zero area (a discrepancy taken into account while making the condition of the surface homologous to the horizons), and therefore the monolayer and the bilayer proposals are equivalent. For, say, the Schwarzschild-de Sitter case, the second layer encounters an ER bridge (since the black hole in say the pode would imply a black hole in the antipode in an entangled state), where the second bottleneck is located. However, we are far from understanding whether there are other information theoretic aspects in de Sitter. In AdS/CFT, presumably things like strong subadditivity can be explained in bit threads, but maybe with semiclassical corrections there are other things to take into account. In de Sitter, this becomes even more complicated. However, this is a nice proposal and I believe some more attention should be given to these things.

Higuchi's Modified norm, Asymptotic WDW states and Refined Algebraic Quantization

In a review I am writing with a collaborator, I am reviewing a bit of Higuchi's proposal (introduced in this paper) for a modified norm. A couple of papers into inspire, I found a very nice set of papers (see this, this and this) that indicated that there was a little more to the story of the group averaging proposal. It was first initiated by Moncrief in his paper ``Space-Time Symmetries and Linearization Stability of the Einstein Equations. 2", where it was conjectured that the infinite norm of a Hilbert space could be modified into a finite norm by dividing by the volume of the group. In the example of the Hilbert space proposal by Suvrat et al [2303.16315], where the asymptotic solutions to the Wheeler-DeWitt equation are of the form

\[\Psi [g, \chi ]=e^{iS[g, \chi ]}\mathcal{Z}[g, \chi ]\;,\]

one has to take into account of the Gauss law, which requires that these WDW states are invariant under the de Sitter isometry group $G_{dS}$. These are of the form (see the paper for a nice discussion about this and a more proper description of how these states are found to be invariant)

Translations: $\tilde{x}^{a}=x^{a}+\epsilon ^{a}$,
Rotations: $\tilde{x}^{a}=R^{a}_{b}x^{b}$,
Dilatations: $\tilde{x}^{a}=\lambda x^{a}$ and
Special conformal transformations: $\tilde{x}^{a}=\frac{x^{a}-\beta ^{a}|x|^{a}}{1-2(\beta \cdot x)+|\beta |^{2}|x|^{2}}$.

For the $t$ coordinate, the above transformations can be found correspondingly. However, if one defines a ``seed" state built on top of the Euclidean vacuum state $|0\rangle $ (called the Bunch-Davies state) by

\[|\mathrm{seed}\rangle =\int dx_{1}\dots dx_{n}\psi (x_{1}\dots x_{n})\chi (x_{1})\dots \chi (x_{n})|0\rangle \;,\]

where $\psi (x_{n})$ is a ``smearing" function with a compact support and $\chi (x_{n})$ are a collection of $n$ massive scalar fields, we see that the only state invariant under $G_{dS}$ (imposed as a constraint) is that of $|0\rangle $. Due to the smearing function, and the nature of the group, the norm $\langle \Psi , \Psi \rangle $ is infinite. This can be interpreted as forming a one-state subspace $\mathcal{H}^{G_{dS}}$ of $G_{dS}$-invariant states from the full Hilbert space $\mathcal{H}$. To correct this, one uses Higuchi's proposal, which proved Moncrief's conjecture, and uses group averaging to define a modified norm

\[\langle \langle \Psi , \Psi \rangle \rangle =\frac{1}{\mathrm{vol}(SO(1, D+1))}\langle \Psi , \Psi \rangle \;,\]

where $\langle \langle \cdot , \cdot \rangle \rangle $ denotes the modified norm (this is somewhat against the usual convention of $(\cdot , \cdot )$, but I will be using this in a different sense below). What one is doing here is defining the space of states formed by group averaging under $G_{dS}$:

\[|\Psi \rangle =\int _{g\in G_{dS}}dg \; U|\mathrm{seed}\rangle \;,\]

where $dg$ denotes the Haar measure and $U(g)$ is a unitary operator. One then has a finite norm set of states which are invariant under $G_{dS}$ isometry group.

In the sense of Refined Algebraic Quantization (abbreviated to RAQ), the whole consideration above reduces into a mathematical problem: given an auxiliary Hilbert space $\mathcal{H}_{aux}$ and a corresponding set of $*$-algebra of observables $\mathcal{A}_{obs}$, one has to find the ``physical" Hilbert space $\mathcal{H}_{phys}$ such that the inner product satisfies the finiteness constraint, and so that the inner product on $\mathcal{H}_{aux}$ is related to $\mathcal{H}_{phys}$. The constraints in the above construction are that the states are invariant under $G_{dS}$, and essentially what we have done is to find the physical Hilbert space, which is a subspace of the initial (in the RAQ terminology, auxiliary) Hilbert space. In the sense of an $\eta $-mapping as discussed in Marolf's paper, one would find a measure so that the following modified norm converges:

\[(\Psi , \Psi )_{\eta }=\int _{g\in G_{dS}} dg\; \langle \Psi |U|\Psi \rangle \;,\]

where $(\cdot , \cdot )_{\eta }$ refers to the modified inner product defined in terms of $\eta $. Group averaging in the above sense of WDW states becomes the norm $(\cdot , \cdot )_{\eta }\to \langle \langle \cdot , \cdot \rangle \rangle $ of $\mathcal{H}_{phys}\to \mathcal{H}^{G_{dS}}$.

Hamilton vs Smale's Poincare Program

The Poincare conjecture was one of the seven Millenium problems that was solved in 2003 by Grisha Perelman in his papers [math/0211159], [math/0303109] and [math/0307245], which showed that when performing Ricci flow on a closed $N$-manifold, it reduces to a type II singularity in finite-time, in the sense that under Ricci flow any closed $N$-manifold is homeomorphic (and diffeomorphic) to $\mathbb{S}^{N}$. This is following the Ricci flow program, initiated by Hamilton (who Perelman stated deserved the Millenium prize, declining upon being told that (1) Hamilton could not be awarded for the complete general proof of Poincare, and (2) since the papers were solely arXived in math.DG and not published, the prize required that he publish the papers if Perelman accepted). While Ricci flow now seems to be the generic approach to Poincare conjecture, in 1961 Smale announced his results that under the h-cobordism theorem, in $N\geq 6$ one can show that for certain kinds of manifolds, using the Alexandrov trick one can show that in general, any closed $N$-manifold is homeomorphic to $\mathbb{S}^{N}$. See my (highly naive) notes on this result, linked below. It must be said that, while the h-cobordism theorem holds for topological and smooth manifolds alike (from Rourke and Sanderson), the Poincare conjecture in Smale's proof need not hold for smooth manifolds. Despite several other reasons why this proof does not hold for all kinds of manifolds (and why this proof fails for certain dimensional cases in $N\geq 6$), I believe that Smale's result was a prime motivator for all the other works leading up to the proof of the Poincare conjecture, whether directly or indirectly. As of the superiority of Hamilton over Smale, I choose to believe that Hamilton's works proved to be far more fundamental and intrinsic to Poincare conjecture (and math.DG) than Smale's work. However, this is only my belief.

Notes on Poincare conjecture and the h-cobordism theorem

Things in hep-th -- Strings 2023 edition

Some topics I am currently reading on, and things to read. Strings 2023 edition.

Algebraic ER=EPR, by Netta Engelhardt. This has not appeared on arXiv yet. Research Talk 20 - Algebraic ER=EPR | PIRSA
A Background Independent Algebra for Quantum Gravity? by Ed Witten. See arXiv [2308.03663] Research Talk 21 - A Background Independent Algebra for Quantum Gravity? | PIRSA
The Hilbert Space of de Sitter Quantum Gravity and Holography of Information, by Suvrat Raju. Based on two papers, [2303.16315] and [2303.16316] Research Talk 16 - The Hilbert space and holography of information in de Sitter quantum gravity | PIRSA
Off-Shell Strings and Black Hole Entropy, by Aron Wall. See [2211.16448] Research Talk 17 - Off Shell Strings and Black Hole Entropy | PIRSA
Cosmic ER=EPR, by Andy Strominger. See [2302.00632] Research Talk 1 - Cosmic ER=EPR | PIRSA
$\text{dS}_{2}$ supergravity, by Beatrix Muhlmann. See [2206.14146] Research Talk 15 - dS_2 supergravity | PIRSA
Irreversibility, QNEC and defects, by Gonzalo Torroba. See [2303.16935] Research Talk 14 - Irreversibility, QNEC, and defects | PIRSA
Bespoke Dual Resonance, by Grant Remmen. See [2308.03833] Research Talk 18 - Bespoke Dual Resonance | PIRSA
Learning in a Quantum World, by John Preskill. Challenge Talk 4 - Learning in a quantum world | PIRSA

Some more works, although I am not aware of these as of yet due to more mathematical complexity. I have included them solely for further interest.

Crossing Beyond Scattering Amplitudes, by Hoffie Hannisdottir. Research Talk 5 - Crossing beyond scattering amplitudes | PIRSA
Feynman's Last Blackboard, by Ed Frenkel. Challenge Talk 2 - Feynman's Last Blackboard: From Bethe Ansatz to Langlands Duality | PIRSA
Emanant Symmetries, by Nathan Seiberg. Research Talk 11 - Emanant symmetries | PIRSA
Revisiting Logarithmic corrections to SUSY-black hole entropy, by Ashok Sen. Research Talk 7 - Revisiting logarithmic corrections to supersymmetric black hole entropy | PIRSA

Thoughts on de Sitter

In the famous 1997 paper by Maldacena [hep-th/9711200] introducing AdS/CFT (which also happens to be the most cited paper in hep-th), the notion of duality between bulk quantum gravity and a CFT on the boundary was found. In some sense, this can be viewed as the equivalence between the gravitational partition function $Z_{\text{grav}}$ and the CFT partition function $Z_{\text{CFT}}$. Some interesting things have also come out of this, most prominently (in my opinion) the calculation of holographic entanglement entropy by Ryu-Takayanagi [hep-th/0603001] and Hubeny-Rangamani-Takayanagi [0705.0016]. Since the inception of AdS/CFT itself, however, people have looked for a dS/CFT correspondence -- a holographic duality between some field theory on the conformal boundary $\mathcal{I}^{+}$ and the bulk gravitating region described by the $D$-dimensional de Sitter space. See for instance, the original paper putting forward dS/CFT by Strominger: [hep-th/0106113]. However, this is something that seems too much of a long-shot, namely, for the following reasons:

Holography at $\mathcal{I}^{+}$ means that the partition function $Z_{\text{CFT}}$ requires non-unitarity, which in some sense can be imagined by the lack of a minimal spacelike geodesic separating two distinct points on the boundary. Therefore, any holographic entanglement entropy proposal would define ``pseudo-entropy" and not something as straightforward as the Ryu-Takayanagi formula. Which of course, one can put up with, but at least for a superficial reason I am petty enough to say that the ``actual" dS/CFT correspondence (if one exists at all) gives a slightly more satisfying description of entanglement entropy than the timelike entanglement entropy - pseudo-holographic entropy equivalence by Harper et al [2210.09457].
Far too many proposals. Again, it might just be that I am being petty with multiple descriptions of holography in de Sitter space, but if a proper description of holography did exist at all, it should be somewhat like AdS/CFT in the sense that the duality is concrete. Right now we have multiple descriptions -- such as global dS/CFT, static patch holography (which is a good enough thing due to things like entanglement entropy calculations and so on), half-de Sitter (introduced just recently by KRST, [2306.07575]), and recently, Cauchy slice holography, which I will talk about in a different post. Perhaps the answer is one of two things: either, that such a correspondence simply does not exist, or that a different kind of holography is to be considered, which would be holography of information from asymptotic quantization.
Finally, because it seems out of bound from a quantum gravity description without supposing things. Which holographic proposal would be have to pay attention to from, say, canonical quantum gravity? The answer for me, seems to be -- none. I have talked below.

What is this aspect of quantum gravity I mentioned that does not work for holography? I cannot make sense of this as of yet, due to some reasons that will be apparent soon. However, if one builds holography in the sense of the GPKW relation,

\[\Psi [g]\sim Z[g]\;,\]

where $\Psi [g]$ satisfies the Hamiltonian and momentum constraints (referred to as a Wheeler-DeWitt state, satisfying the annihilation of the Hamiltonian constraint or the Wheeler-DeWitt equation) and $Z[g]$ is a CFT partition function in dS. Now, here is the question: if one assumes this to be true (which is, for well-known case of the Hartle-Hawking state), what is the Hilbert space of dS quantum gravity? One could suppose to do Cauchy slice holography [2204.00591], which for AdS/CFT works amazingly -- you start from the CFT partition function and use a $T\overline{T}$-deformation to move into a bulk Cauchy slice, and identify holographic duality between $\Psi [g]$ and the deformed partition function $Z^{\Sigma }[g]$. Note a thing above, which is that I have not mentioned the dependence of $\Psi [g]$ or $Z[g]$ on matter contributions -- if we consider the case of gravity coupled to a massive scalar field, one would have in those contributions as well, but for the sake of discussion I have not included it. For de Sitter, this deformation from the boundary $\mathcal{I}^{+}$ is not clear, at least for me. But even if one does identify these things, which holographic proposal would we derive? Static patch? Global dS/CFT? This is not clear for me yet. But even if this is clear, this does not answer the question, ``what is the Hilbert space of de Sitter quantum gravity?" This was answered just recently (discussions on which I was fortunate to hear before the paper was arXived at lunch at ICTS) in a paper by Suvrat and collaborators [2303.16315], which is a nice result, and this uses asymptotic quantization, which is to work with late-time slices (essentially by identifying a conformal factor $\Omega $ in the metric so as to identify an intrinsic ``clock" or York time) instead of $\mathcal{I}^{+}$. This has a nice result, that in some sense one has a proper identification of the WDW states in de Sitter. However, more on this later.

John Baez's paper on Hoang Xuan Sinh’s Thesis

On my reading list is the paper by John Baez that came out just today. While I am not very familiar with Category theory, I find this to be an interesting read. This is on Hoang Xuan Sinh's thesis work that she did with Grothendieck, knowing him from his teaching weeks during the Vietnam war near Hanoi.

[2308.05119] Hoàng Xuân Sính's Thesis: Categorifying Group Theory (arxiv.org)

Open access in journals and Conditional publication

An Essay I wrote for GRF competition entitled ``Holographic Quantum Gravity and Horizon Instability" [2304.01292], received an ``honourable mention". What is strange, is that I was invited to publish with a particular (quite well-reputed) journal, on the condition that I shorten it down to two pages. I agree that my Essay was very tersely written and awkwardly close to Engelhardt and Horowtz's paper on the No Transmission Principle (I am planning on revising it by about September with some further aspects; initially, the paper was supposed to contain some more mathematics on SCC and include NTP, but was asked to first shorten to less than 10 pages), but on the basis of publications it seemed a little strange that two pages was the condition put on a paper elaborating a substantial work (a revised version is what was submitted, rather than the arXived version which is not the current version). In fact, I was told by a colleague that the initial and final (arXived) versions of the essay had some differences, making it look as if the point of the paper was more or less to superficially include the NTP paper. Maybe this condition was to let more papers on the GRF edition be added, but I am now forced to doubt the quality of papers being published under such conditions.

One of the reasons I read journals (mostly either JHEP or PRD) is to make sure that calculations in a particular paper I read on arXiv are correct when I cannot hand-check them. But if there are chances that papers are forced to shorten or so, it would definitely affect quality and brush aside details that may be negligible for someone but subtly significant for someone else. Not to mention open access in general is something of a worry; to read a paper, one requires either an institutional subscription to the journal, or is hidden behind a paywall. Such things in the academia seem a little bothersome, especially for people who are in early career works who do not have grants/funding. It is for these reasons that arXiv is a very commendable effort, considering that they do not have any processing charges and is fully open access, as opposed to journals that have open access only if the submitting author pays a charge (for myself, the SCOAP initiative is a good effort alongside arXiv in the field of hep-th that helps in preventing out-of-pocket money from being used). Publishers like Springer and APS should have options so that authors from any field have an option for free publication. I understand their necessity due to on-paper publication, but at least for those who do not have any grants or opt in for solely online publication, such an option should be available. And as of the conditional publications during peer-review or desk editor requirements, these interfere directly with the content of a work, and this is something that should be taken more seriously.

Strings talk at ICTS

I had given a talk on ``Aspects of the Generalized Second Law and the Covariant Entropy Bound" at ICTS-TIFR today in the afternoon. While it didn't go well (forgot a $-$ sign in the QNEC formula and was too nervous to realise it), I got some nice discussions with Suvrat and Loganayagam on some of these things. It must be in mind that, I wanted to also talk about the quantum Penrose inequality result by Bousso et al. However, I did not want to bring about this controversial subject about the nature of spacelike foliations, quasi-local mass and the un-dynamic nature of such a formula in the talk, due to which I deferred to talk about this. I also did not discuss on holographic screens and hyperentangled regions, so the main results of the paper were not pointed out. Partly, this was so since the version of the paper arXived is an old one, and the actual version of the paper has not been written as of yet. However, this was a nice discussion, and I will post the YouTube link once it is archived (if so at all).

Edit: The talk is available on the ICTS Strings seminars channel at Vaibhav Kalvakota - Aspects of the Generalized Second Law and the Covariant Entropy bound.

Paper by Bousso and Pennington

A paper by Bousso and Pennington titled ``Holograms in Our World" has been arXived today.

[2302.07892] Holograms In Our World (arxiv.org)

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