Abstracts

Sergei Alexandrov: Mock modularity of BPS black holes

I'll explain the modular properties, and their physical origin, of the generating functions of D4-D2-D0 BPS indices counting black hole states in Calabi-Yau compactifications of string theory. These properties can be used to find generating functions up to a finite number of coefficients, the so-called polar terms, which in turn can be fixed using wall-crossing. I'll show how this program is realized for compact one-parameter Calabi-Yau threefolds and 2 units of D4-brane charge, leading to explicit mock modular forms encoding BPS indices. For higher charges, the polar terms remain so far inaccessible, but I'll present a general solution of modular anomaly equations in terms of indefinite theta series.

Luis Apolo: Logarithmic corrections to black hole entropy from weak Jacobi forms

In this talk, I will describe the asymptotic growth of states of weak Jacobi forms (wJfs) with features motivated by the AdS3/CFT2 correspondence. The asymptotic growth of such wJfs is known to be given by Cardy's formula, which reproduces the entropy of certain BPS black holes. l will show how the distribution of light states affects the regime of validity of the Cardy growth of states. Then, I will consider the subleading corrections to Cardy's formula and describe the conditions for which these corrections are universal or sensitive to the distribution of light states. In the context of black holes, these corrections correspond to logarithmic corrections to their entropy, and I will show how these logarithmic corrections can be reproduced from wJfs in different scenarios.

Nathan Benjamin: Angular fractals in thermal CFT

I will discuss universal properties of partition functions at high temperature and large angular fugacity in d>2 conformal field theories (CFTs). This provides spin-refined information -- namely the statistics of spins of local operators -- valid for all CFTs, that in some sense generalizes modular invariance of d=2 CFTs. As an example application, I will show that the effective free energy of even-spin minus odd-spin operators at high temperature is smaller than the usual free energy by a factor of 1/2^d. Based on arXiv:2405.17562.

Nana Cabo Bizet: Type IIB strings on 1-parameter Calabi-Yau manifolds and quantum gravity conjectures

We explore the refined de Sitter conjecture (RdSC), the Trans-Planckian Censorship Conjecture (TCC), and the species scale ($L_s$) in the multifield flux potential of type IIB strings on one-parameter Calabi-Yau manifolds. The scalar potential depends on the axio-dilaton and complex structure, with non-scaling directions for the Kähler moduli. For numerical analysis, we focus on geometries with Hodge numbers $(h^{2,1}, h^{1,1}) = (1,101), (1,4), (1,1)$. Our search for de Sitter vacua shows that the RdSC holds with 96% accuracy, even with the inclusion of one Kähler modulus. We examine the TCC by computing the potential in terms of the affine parameter for multifield evolution, finding consistency in asymptotic regions of the moduli space (large complex structure, small $g_s$, large axion). The scalar field displacements respect the $L_s$ bound. We conclude that this region is fertile within the landscape, and we outline a machine learning approach to pursue scans of these models.

Abhishek Chowdhury: Counting N=8 black holes as algebraic varieties

We calculate the helicity trace index B_14 for N = 8 pure D–brane black holes using various techniques of computational algebraic geometry and find perfect agreement with the existing results in the literature [1]. For these black holes, microstate counting is equivalent to finding the number of supersymmetric vacua of a multi–variable supersymmetric quantum mechanics which in turn is equivalent to solving a set of multi–variable polynomial equations modulo gauge symmetries. We explore four different techniques to solve a set of polynomial equations, namely Newton Polytopes, Homotopy continuation, Monodromy and Hilbert series. The first three methods rely on a mixture of symbolic and high precision numerics whereas the Hilbert series is symbolic and admit a gauge invariant analysis. Furthermore, exploiting various ex- change symmetries, we show that quartic and higher order terms are absent in the potential, which if present would have spoiled the counting. Incorporating recent developments in alge- braic geometry focusing on computational algorithms, we have extended the scope of one of the authors previous works [2, 3] and presented a new perspective for the black hole microstate counting problem. This further establishes the pure D–brane system as a consistent model, bringing us a step closer to N = 2 black hole microstate counting.

• [1]  Abhishek Chowdhury, Sourav Maji. Counting N = 8 black holes as algebraic varieties. JHEP, 05:091, 2024.

• [2]  Abhishek Chowdhury, Richard S. Garavuso, Swapnamay Mondal, and Ashoke Sen. BPS State Counting in N=8 Supersymmetric String Theory for Pure D-brane Configurations. JHEP, 10:186, 2014.

• [3]  Abhishek Chowdhury, Richard S. Garavuso, Swapnamay Mondal, and Ashoke Sen. Do All BPS Black Hole Microstates Carry Zero Angular Momentum? JHEP, 04:082, 2016.

Chandramouli  Chowdhury: Simplicity of In-In correlators in dS

We compute loop integrals of in-in correlators in dS for scalar theories and comment on the nature of the functions encountered and a new hidden simplicity in dS correlators as compared to loops of AdS correlators.

Based on upcoming work and 2312.13803, 2408.00074.

Ben Craps: Factorization of the Hilbert space of eternal black holes in general relativity

I will use the Euclidean gravity path integral to argue that the Hilbert space of eternal black holes factorizes in quantum gravity with a negative cosmological constant in any dimension.  I will approach the problem by computing the trace of two-sided observables as a sum over a recently constructed family of semiclassically well-controlled black hole microstates. These microstates, which contain heavy matter shells behind the horizon and form an overcomplete basis of the Hilbert space, exist in any theory of gravity with general relativity as its low energy limit. Using this representation of the microstates, to leading order in the semiclassical limit, I will show that the trace of operators dual to functions of the Hamiltonians of the left and right holographic CFTs factorizes into a product. Under certain conditions these results imply factorization of the Hilbert space.

 Bartek Czech: Two-Sided Differential Entropy

In the AdS3/CFT2 correspondence, a boundary quantity called differential entropy computes the area of a non-extremal bulk surface, which wraps around the black hole horizon. I present a generalization of differential entropy, which can simultaneously describe surfaces that live on either side of a two-sided black hole. The formula derives from recently discovered holographic entropy inequalities, which form facets of the holographic entropy cone. Interestingly, the formula has a topological origin and reflects non-trivial topological facts about the phase diagram of Ryu-Takayanagi surfaces.

James Halverson: Conformal fields from neural networks

We use the embedding formalism to construct conformal fields in D dimensions, by restricting Lorentz-invariant ensembles of homogeneous neural networks in (D+2) dimensions to the projective null cone. Conformal correlators may be computed using the parameter space description of the neural network. Exact four-point correlators are computed in a number of examples, and we perform a 4D conformal block decomposition that elucidates the spectrum. In some examples the analysis is facilitated by recent approaches to Feynman integrals. Generalized free CFTs are constructed using the infinite-width Gaussian process limit of the neural network, enabling a realization of the free boson. The extension to deep networks constructs conformal fields at each subsequent layer, with recursion relations relating their conformal dimensions and four-point functions. Numerical approaches are discussed.

Elli Heyes: Machine-Learning G2 Geometry

Kaluza-Klein reduction of 11-dimensional supergravity on G2 manifolds yields a 4-dimensional effective field theory (EFT) with N=1 supersymmetry. G2 manifolds are therefore the analog of Calabi-Yau (CY) threefolds in heterotic string theory. Since 2017 machine-learning techniques have been applied extensively to study CY manifolds but until 2024 no similar work had been carried out on G2 manifolds. We first show how topological properties of these manifolds can be learnt using simple neural networks. We then discuss how one may try to learn Ricci-flat G2 metrics with machine-learning. 

Luca Iliesiu: Flatspace holography for supersymmetric indices 

I will describe novel black hole and black string solutions in supergravity that can be used to compute supersymmetric indices in flatspace. Surprisingly, even though such solutions do not rely on the traditional decoupling limit taken in AdS/CFT but rather exist at finite temperatures in flatspace, they still capture the protected index of conventional supersymmetric quantum theories, including that of SCFTs.

Vishnu  Jejjala: Precision String Phenomenology

Calabi-Yau compactifications of string theory lead to quantum field theories in four dimensions with chiral matter. Calculating parameters of the low-energy effective theory in general compactifications requires the Ricci-flat metric on the Calabi-Yau manifold. Such metrics are not known analytically. In this talk, we discuss how to approximate the Ricci-flat metric using neural networks. The accuracy of the numerical metrics is assessed for K3 and the quintic threefold. In the standard embedding, we calculate Yukawa couplings for compactifications on various Calabi-Yau geometries. This is an initial step toward a first principles calculation of particle masses from string theory.

Abhiram Kidambi: On arithmetic statistics of Hecke eigenforms of weight two

I will start with the essentials of elliptic curves, their symmetries, arithmetic, and zeta functions. I will then go over how experimental number theory is still discovering new things about the arithmetic of elliptic curves. Finally I will present observations on arithmetic statistics of hecke eigenforms attached to elliptic curves.

Proofs will be omitted and available in the upcoming paper.

Robert de Mello Koch: Constructive Holography

We argue that collective field theory provides a constructive approach to gauge theory/gravity dualities. In particular a detailed holographic map which gives a one-to-one map between physical and independent degrees of freedom of the gravity and independent degrees of freedom of the original conformal field theory is derived. As is well known, the collective field theory description is overcomplete, leading to a redundant description. We argue that this redundancy is the origin of holography i.e. that there is a complete set of degrees of freedom at the boundary of the gravitational theory.

Swapna Mahapatra:

We consider the dimensional reduction to two dimensions of certain gravitational theories in D ≥ 4 dimensions at the two-derivative level. It is known that the resulting field equations describe an integrable system in two dimensions which can also be obtained by a dimensional reduction of the self-dual Yang-Mills equations in four dimensions. We use this relation to construct a single copy prescription for classes of gravitational solutions in Weyl- Lewis-Papapetrou coordinates. We also disccuss the gauge group of the Yang-Mills single copy which carries non-trivial information about the gravitational solution. We illustrate our single copy prescription with various examples that include the extremal Reissner-Nordstrom solution, Kaluza-Klein rotating attractor solution, Einstein-Rosen wave solution and self-dual Kleinian Taub-NUT solution. We also discuss the single copy description of the Eguchi-Hanson solution.

Dmitry Melnikov: Error-Correcting Codes in TQFT on Multispheres

Topological quantum field theories (TQFT) encode quantum correlations in topological features of spaces. In my talk I will apply this feature to explore how information encoded in TQFTs can be stored and retrieved in the presence of local decoherence affecting its physical carriers. TQFT states' inherent nonlocality, redundancy, and entanglement make them natural error-correcting codes, which, among other things, provide an alternative perspective on the relation between error-correcting codes and holography. I will demonstrate that information recovery protocols can be derived from the principle that protected information must be uniformly distributed across the system and from interpreting correlations in terms of space connectivity. Specifically, we employ a topological framework to devise erasure error correction protocols, showing that information can be successfully recovered even when parts of the system are corrupted.

Thomas Oliver: Murmurations of Dirichlet characters

Murmurations are unexpected statistical correlations between the coefficients of L-functions and their root numbers. Murmurations were first discovered in attempts to interpret the accuracy of various machine learning experiments in number theory. Dirichlet characters are an interesting context as they allow one to state and prove concrete theorems with easily understandable tools. In this talk, I will show how the "murmuration density" allows one to capture the signal in a noisy arithmetic picture, and how this density interpolates the one-level density of their zeros.

Damián Mayorga Peña: Classical integrability in the presence of a cosmological constant: analytic and machine learning results

We study the integrability of two-dimensional models arising from the dimensional reduction of four-dimensional theories describing the coupling of Maxwell fields and neutral scalars to gravity in the presence of a potential for the neutral scalar fields. In the absence of this potential, the integrability of the system is captured by the Breitenlohner-Maison (BM) linear system. In this talk, we focus on a solution subspace for the models with a scalar potential and write down a linear system, whose compatibility equations are a subset of the two-dimensional equations of motion. Further we consider the reduction of the aforementioned models to one dimension and discuss their Liouville integrability in the language of Lax pair matrices and conserved currents. For these one dimensional models we implement two machine learning strategies, intended to predict such Lax pair matrices and conserved currents. We compare our findings to our analytical results. Finally we discuss the broader scope of these machine learning approaches in helping to identify integrable structures in general one dimensional classical systems.