Strange But Charming

Odyssey Sketchbook | Odysseus demo 1

Here is the track I had composed for Odysseus. Upcoming tracks will be released in the coming weeks.

Things I Wish to Understand.

Here is a list of things that I do not understand that I wish to learn about in the coming months.

Spinorial formalism in string compactifications.
String field theory, I started on the review by Sen and Zweibach.
Moduli spaces and Riemann surfaces.
Random matrices, JT gravity and topological recursion.
Explicit $\mathcal{N}=2$ supergravity constructions.
More on Hodge numbers and moduli stabilisation.
Computing superpotential contributions from F-theory.
Explicit F-theory constructions of any sort lolz.
Anything compactifications in heterotic string theory.
AdS/CFT in KKLT AdS construction: what happens when you break SUSY?
Compute pfaffians.
Fully read Ashoke's orientifolds/F-theory limits paper.
Understand Gopakumar-Vafa invariants.
BPS states, logarithmic corrections, etc.
$\alpha '$ corrections to KKLT/LVS scenarios.

Perhaps it is time to dig into each of these now that it is my summer break.

String compactifications review! (Anti-Quill Part 7)

A review paper I have been collaborating with Aayush Verma has finally been completed. It is a review on string compactifications and the essentials of it. It covers Kaluza-Klein compactifications, string compactifications, moduli stabilisation, flux compactifications and de Sitter compactifications, mostly centred around the KKLT construction with type IIB SUGRA. It has been a 4-month work in progress that is still not fully complete, but it is a pretty decent paper with some bits of humour. I learnt a lot, and there have been some really fun conversations around such de Sitter problems. Enjoy!

REVERING MUSINGS ON STRING COMPACTIFICATION (BUT MOSTLY DE SITTER)

Blade Runner 2099 Sketchbook | Tears In Snow

Here is the first track in my Blade Runner 2099 Sketchbook, called Tears In Snow.

Blade Runner 2099 Sketchbook | Tears In Snow - Vaibhav Kalvakota

Anti-Quill Part 6: Type IIB and F-theory -I

I genuinely forgot that I had a blog. Anyway, here is a short post on F-theory/M-theory duality. Inherently, type IIB superstring theory comes with a bundle of data like D-branes, O-planes and fluxes. I have mentioned how these play an important role in stabilising the moduli. We are yet to talk on the exact nature of these moduli stabilisations and especially in view of fluxes. But first, a short note on the axiodilaton, which is given by the RR field $C_{0}$ and string coupling $g_{s}$:

\[\tau = C_{0}+ig_{s}^{-1}\;.\]

This axiodilaton can be thought of as the modulus of elliptic fibration when KK-compactifying M-theory into type IIA theory, and performing a T-duality action on this type IIA theory gives you your type IIB theory back. That is, taking M-theory on $\mathbb{R}^{9}\times S^{1}\times S^{1}$ with some $R_{S^{1}}\to 0$, you obtain type IIA theory on $\mathbb{R}^{9}\times S^{1}$. Then, acting on this with T-duality gives us $\mathbb{R}^{9}\times \mathbf{S}^{1}$ type IIB theory, and in $\mathbf{R}_{S^{1}}\to \infty $ we get $\mathbb{R}^{10}$. The following tables are from nlab and the TASI lectures by Weigand respectively, which are helpful.

I'll type more in a minute. Btw I saw Dune Part 2 yesterday from 1320 to 1620 hrs. After 114 viewings, it is more golden than before.

Interstellar on IMAX

I watched Interstellar on IMAX today from 1315 to 1615 hrs. Wow I just can't express how much I love it. Interstellar and Dune will forever be the only things that I hold close to me more than anything.

Anti-Quill Part 5: D-Branes and O-planes 1

In Anti-Quill Part 4, we discussed Calabi-Yau manifolds and the essential idea of compactifications on them. Before going forward, it is important to note that a lot of care has to be taken in ensuring SUSY and structures are preserved. As an example, take a type IIB theory on $T^{6}=T^{2}\times T^{2}\times T^{2}$. We have two fluxes, the NS-NS fluxes $H_{3}$ and the RR flux $F_{3}$. If you define an involution operator $\pi : (z)_{3}\to (-z)_{3}$, the fixed points of $\pi $ would correspond to the O3-planes along with the parity conjugation operator $\mathcal{P}$. This has the effect of taking $p$-forms and turning them into -$p$-forms under $\pi $, after which we act with $\mathcal{P}$. In order for $H_{3}$ and $F_{3}$ to be of the same parity after the action of $\mathcal{P}\cdot \pi $, they must have odd parity under $\pi $, so that they have consistent parity with the O3-planes. Having said this, it is a nice simple exercise to convince yourself why this is important in view of tadpole cancellation. Another interesting exercise from van Riet is to take $T^{6}$ with angles $\theta _{i}$ and $\pi _{O3} : \theta _{i} \to -\theta _{I}$, with 64 O3-planes. Taking a simple $F_{3}$ flux $F_{3}=d\theta _{1} \wedge d\theta _{2}\wedge d\theta _{3}$, for dilaton stabilisation, what would be the corresponding $H_{3}$ flux?

Anti-Quill Part 4: Calabi-Yau 2

In Anti-Quill Part 3, we recalled some interesting properties of Calabi-Yau manifolds. Since a Calabi-Yau metric $g$ can be perturbed via some deformation $g+\delta g$ continuously to produce another Ricci flat manifold, this gives us a moduli space of CY manifolds. Using hodge diamond and specifically calculating hodge numbers with quintic hypersurfaces $\Sigma $ in $\mathbb{CP}^{4}$, one can find the dimension of the moduli space. In string theory, the actual nature of the moduli space is far more complicated because we want to do EFTs and somehow quantify viable vacua (if they exist!). The swampland distance conjecture tells you that taking two points on the moduli space $M(\text{string theory})$, there is an infinite tower of modes with exponentially vanishing mass: $M \sim m\exp (-\lambda s)$, where $s\to \infty $ is the geodesic distance on $M(\text{string theory})$. We expect usually that the ``landscape" theories lie in a particular part of this moduli space and the UV-complete nature of it, and how EFT corrections contribute in certain limits, like when $g_{\text{string}}$ is weak. There are some subtleties around how you view the converse with the light tower of modes, see van Riet and Zoccarato. However, the full moduli space even geometrically is non-trivial. Addition of fluxes with the split $M=M_{c}\times M_{K}$ from before is done by the Gukov-Vafa-Witten superpotential $V_{GVW}(\Omega _{3}, G_{3})$, where $\Omega _{3}$ is the complex structure moduli and $G_{3}$ is the dilaton.

Anti-Quill Part 3: Calabi-Yau 1

In Anti-Quill Part 2, I mentioned how we add in D-branes and O-planes into the theory and not just the moduli and the fluxes. The way we gauge whether or not a given theory has viable compactifications is by looking at the effective potential for phenomenological reasons. As an example, the Freund-Rubin effective potential is

\[ V \sim \frac{1}{R^{4}} \left( \frac{2g-2}{R^{2}}+\frac{N^{2}}{R^{2}} \right)\;, \]

where $N$ are the number of fluxes. However, Freund-Rubin are not complete or realistic compactifications (even if you add in perturbative corrections). One way in which you could see this is to note that $g$ is not zero for compactifications we wish to pursue (Candelas et al). We instead wish to work with Calabi-Yau manifolds, which are Kahler manifolds with $c_{1}(K_{M})=0$, where $K_{M}$ is the complex line bundle. Very quickly, we will notice two interesting features. To start, see that $T^{2}$ can be decomposed into to two $S^{1}$ with radii $(r_{1}, r_{2})$, and the moduli space for this would be a 2-dimensional manifold $M(r_{1}, r_{2})$. Defining $\tau = iT$, where $T=R_{2}/R_{1}$, notice that there is a $T$-duality, which more generally is a mirror symmetry for reasons I will defer from here. In string theory, one usually also adds in a $B$-field, but the point here is that Calabi-Yau manifolds have this $T$-duality. For general moduli spaces $M_{D}$ of Calabi-Yau manifolds, we define a Weil-Petersson metric $g_{WP}$, which is a Kahlerian metric on $\mathrm{Teich}(n, g)$. An interesting associated result is that the Weil-Petersson volume $V_{WP}(M)$ is finite, and that $R(g_{WP})$ for $M(CY3)$ is either positive or negative, unlike for general $M(K3)$ (something I am still trying to understand). It is then of interest how the curvature and the Weil-Petersson metric affect the stringy moduli space, which typically decomposes into $M=M_{c}\times M_{K}$.

Anti-Quill Part 2: Orientifolds

Like I said in Anti-Quill Part 1, when doing compactifications we also have to consider D-branes and O-planes. These orientifolds are quite mysterious; in a mathematical context, these arise from RR tadpole cancellation in type IIA/B superstring theories and are related to orbifolds. For now, however, we will approach orientifolds from the second and the more characteristic nature of orientation reversal. To see this, recall that strings on the worldsheet in closed string theories decompose into left and right moving modes $X^{\mu }_{L}(t+\sigma )$ and $X^{\mu }_{R}(t-\sigma )$. With periodicity $\pi $, we can introduce a parity conjugating operator $\mathcal{P}$ so that $\mathcal{P} : X^{\mu }_{L}(t+\sigma )\to X^{\mu }_{R}(t-\sigma )$. In the grand scheme of M-theory, you have the duality between type IIA and type IIB superstring theories via the T-duality, and you can relate type I superstring theory to type IIB and conversely type IIA by using a combination of T-duality and the action of $\mathcal{P}$. In this sense, taking an un-oriented version of type I string theory on $S^{1}$ and acting on it with T-duality gives you a type IIA string theory. In this language of O-planes, a type I theory is a type IIB theory with an O9-plane, whereas with type IIA theory it would be an O8-plane. Going from type IIB to type I theory, the O-planes break half the supersymmetry of the full theory.

Anti-Quill Part 1: Compactifications

This is the $CPT$-conjugated version of Aayush's very good Quill series. My series is conjugated in the sense that I won't be as mathematical or elaborate or excessively (and frankly concerningly) obsessed with algebraic geometry.

In string theory, compactifications reduce to the usual 4D Einsteinian gravity in the low energy limit, with an ``external" (although usually this is considered the internal space) manifold $K$ with the extra dimensions surpassed into a small scale similar to the $S^{1}$ with small $r$ in Kaluza-Klein compactifications. In our case, 10D string theory would be $M_{4}\times K^{6}$ with Ricci flatness and a more special condition, that the first Chern class $c_{1}=0$. These lead us to Kahler manifolds and more specifically, Calabi-Yau manifolds. In general, what comprise compactifications are the following: moduli of massless scalar fields, a moduli space of geometries admissible under these moduli, addition of fluxes $\mathcal{F}$ from the theory, D-branes contributing with positive $T$ and orientifold planes contributing with negative $T$. The last three are a messy subject in an EFTs sense because of the tadpole cancellation conjecture in the swampland. A very simple example of stringy compactifications (although not very realistic here because we ignore perturbative corrections) is that of Freund-Rubin compactifications, where you can take magnetic fluxes across $S^{2}$ and write the effective potential in terms of the addition of these fluxes. This is usually an order $\sim 1/R^{6}$ (where $R$ is the volume modulus) against the genus $g$, but the negative curvature contributions are cancelled out when the number of fluxes $N$ is large. When you have large fluxes, these do much to ``stabilize" the moduli against the negative curvature contributions and in more complicated theories, these fluxes being used for moduli stabilization tells you a lot about the EFT and vacua. A similar philosophy applies to more realistic stringy scenarios. In type IIA superstring theory, you add in O-planes and D-branes as well, but with caution since you have to worry about tadpole cancellation. This is typically a problem in F-theory where Calabi-Yau 4-folds are stabilised, but with fluxes adding to the D3-brane tadpole.

Strings 2025 page

Here is the Strings 2025 page I made:

Strings 2025

Strings 2025: Day 5 The End

Unfortunately, Strings 2025 has come to an end. I really dread this feeling after so much of learning, interesting talks, and exposition of awesome research by awesome people, and I dearly miss the daily talks and sessions. However, Strings 2026 is to be announced and I am personally urging my theoretical physicist friends to please, step forward and propose for Strings 2026. This amazing conference should not be allowed to stagnate and the amazing field that is string theory must be worked on.

There are many pictures that I took and therefore will be uploading only a few on this post; I missed several talks today, but the entire gallery of pictures I have taken will be uploaded and updated on this blog. To string theory, to Strings, and to the amazing organisers at NYU Abu Dhabi!

Ahmed giving the conclusion and final remarks.

Flowers!

Castro feels flipped out with de Sitter

Geoff Penington talk.

Do your quantum mechanics, people.

Hi Geoff!

Shiraz kidnapped the microphone.

Shiraz and David Gross

Only four panelists at the end.

Mr. David Gross himself.

Leaving panelists

Panel

Proud Almheiri, and he believes in Strings 2026!

Juan is talking in the panel discussion.

The last picture I took of the Strings meeting. Really sad.

Strings 2025: Day 4 de Sitter

Today was concluded with Sandip's talk, which I enjoyed very much. I found Anninos' talk very good too, and there are quite a few pictures I took. However, I will limit how many I post right now and instead have a dedicated Strings 2025 gallery page up by tomorrow.

Hi Anninos

Deformed CFTs.

Anninos' talk was very interesting.

Cumrun had a question just then

Holography and $T\overline{T}+\Lambda _{2}$ deformations.

de Sitter static patch.

I couldn't hear him for a while because I had my speakers on low volume. Dumb me,

Hello Sandip!!

Juan had a question in Anninos' talk.

Juan still asking the question he talked about with Verlinde.

Naomi's talk.

I think this was during Anninos' talk as well.

Suvrat had a question about the semiclassical limit.

Sandip pointing to references.

Zamolodchikov OP in the chat!!

Sandip's talk was awesome!

About the Hartle-Hawking state and double-scaled matrices.

Ed had a question right after Suvrat.

Eva had a question too!

Really interesting talk on de Sitter JT gravity.

Strings 2025: Day 3 Conclusion

Sorry I am late to posting these pictures, I was watching The Intern with mom. Note that these pictures are not in a chronological order and I am uploading from my phone. I also did not attend Vishnu's talk on CY metrics either.