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:

1. 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. 
2. Operator algebras. In all sorts of places, most strikingly in AdS/CFT.
3. 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.
4. de Sitter space. For instance, Chandrasekharan, Longo, Pennington and Witten recently worked on static patch algebra of observables and type II$_{1}$ algebras.
5. Information problem and islands. 
6. Topological QFTs.
7. 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.

• Bismarck vs Hood original WWII recordings footage
• Destroyer Life in the Pacific 1943-44
• U-Boat in color 1
• Battle of Jutland footage in colour
• WW2 - The Battle of the Atlantic [Real Footage in Colour]

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.

• [0806.1079] AQFT from n-functorial QFT,
• [math-ph/0112041] The generally covariant locality principle -- A new paradigm for local quantum physics,
• [2311.03443] The S-matrix and boundary correlators in flat space,
• [2311.02301] Geometrizing the Partial Entanglement Entropy: from PEE Threads to Bit Threads,
• [2311.07934] Duality in Gauge Theory, Gravity and String Theory,
• [2311.06940] On the Hawking mass for CMC surfaces in positive curved 3-manifolds,
• [math/0105018] Homotopy Quantum Field Theories and the Homotopy Cobordism Category in Dimension 1+1,
• [2311.04281] Algebraic ER=EPR and Complexity Transfer,
• [2110.05470] Failure of the split property in gravity and the information paradox.

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.