The TTbar deformation is an irrelevant deformation of 2D field theories associated with nonlocal UV behaviour. Despite its apparent solvability, many aspects of the deformation remain mysterious. In this talk, I will present exact results for the TTbar deformation of 2D U(N) Yang-Mills theory. Carrying out the analysis at the level of each instanton sector, we can determine the nonperturbative contributions to the partition function and prove that the spectrum undergoes a truncation (a property only conjectured for other TTbar-deformed theories). We then derive the large-N limit by studying the relevant flow equation, uncovering a rich phase diagram where phase transitions are driven by instanton condensation.

The Bekenstein-Hawking entropy of 1/16-BPS AdS_5 black holes is captured by a superconformal index. Such indices exhibit SL(3,Z) modular properties, which are explicated in terms of ambiguities in the Heegaard splitting of an associated Hopf surface. We conjecture a "modular factorization" of superconformal indices of general N=1 gauge theories and provide evidence for this conjecture by studying the free chiral multiplet and SQED.

Long range entanglement is a conceptually useful notion in the physics of quantum phases of matter. E.g. in (2+1) dimensions, ground states display area law entanglement with a potential constant correction: the "topological entanglement entropy" (TEE) which is a smoking gun of topological order. Through the lens of the IR effective field theory, described by topological quantum field theory (TQFT), we encounter the following puzzle: how does a field theory with a finite dimensional Hilbert space support a divergent area law? The simple resolution to this puzzle will also suggest an alternative perspective on topological entanglement. Utilizing the algebraic formulation of entanglement I will define a quantity I will call "essential topological entanglement." It is (i) strictly topological, (ii) positive, (iii) finite, and (iv) displays more long-range features than traditional TEE. Working with Abelian p-form BF theory as an example, I will explain general aspects of essential topological entanglement. I will elaborate on potential further applications of essential topological entanglement, as well as describe some follow-up work regarding the entanglement carried by edge-modes in BF theory.

In this talk I will provide briefly summarize the status of numerical lattice simulations of supersymmetric gauge theories. As an example I will focus on low dimensional supersymmetric Yang-Mills theories in the context of gauge/gravity duality.

Decoherence and thermalisation of isolated many-particle quantum states are studied in many different subfields of physics, including high-energy physics. One of the most interesting case are Heavy Ion Collisions which can be holographically connected to string theory in Anti-de Sitter space and for which very detailed data exists. After a general introduction I will focus on the question whether SU(N) gauge theories behave as predicted by the Eigenstate Thermalization Hypothesis (ETH). To answer this question we have performed simulations for low-dimensional SU(2) gauge theories on digital computers (arXiv: 2308.16202) which gave encouraging results. As ETH makes predictions for energy eigenstates the most natural theoretical approach to study e.g. thermalization of QCD is the numnerical simulation of Hamiltonian lattice QCD on quantum computers which, however, is not yet possible. Investigating the validity of ETH on digital computers is an early step in this direction.

We consider black hole linear perturbation theory in a four-dimensional Schwarzschild (anti-)de Sitter background. We describe two methods that provide the quantization condition for the quasinormal mode frequencies of the perturbation field. The first consists of using the Nekrasov-Shatashvili functions, or, equivalently, the classical Virasoro conformal blocks, to obtain the connection coefficients for the differential equation encoding the spectral problem. The second method is based on a perturbative expansion of the local solutions of the differential equation, that involves multiple polylogarithmic functions. We conclude by showing how the two methods shed light on the mathematical structure of the quasinormal mode frequencies, and discussing how they can be generalized to problems in different backgrounds, emphasising their effectiveness.

Tambara-Yamagami (TY) 1-categories provide the mathematical framework to describe the algebra of extended operators of (1+1)-d theories that admit a duality defect. In this talk I will define what is the generalization of TY 1-categories for fusion 2-categories, and how to construct them from fusion 2-categories that are group-theoretical. I will also explain that group-theoretical fusion 2-categories are completely characterized by the property that the braided fusion 1-category of endomorphisms of the monoidal unit is Tannakian. Using this characterization, I will show when a fusion 2-category admits a fiber 2-functor.

String theory has far surpassed expectations in its ability to shed light on many areas of theoretical and mathematical physics. However, partly due to the immense size of the solution space, it is yet to be determined if our universe lives somewhere in the string landscape. In this talk, I will present how methods from computer science (genetic algorithms and reinforcement learning) can shed some light on these questions by exploring promising regions of the string landscape. Specifically, reinforcement learning and genetic algorithms are used to construct sums of line bundles and monad bundles on smooth Calabi-Yau threefolds, for compactifications of E8xE8 heterotic string theory.

In this talk we will attempt to reconcile two different results on two-dimensional pure Yang-Mills theory. Specifically, we will discuss how the fact that 2d pure Yang-Mills is equivalent to a disjoint union of theories, is related to the Gross-Taylor description of 2d pure Yang-Mills as the target-space field theory of a string theory. The Gross-Taylor picture can be understood by first rewriting the Yang-Mills partition function (in a large N limit) as a sum of correlation functions in Dijkgraaf-Witten theories for the symmetric group S_n, and then interpreting those Dijkgraaf-Witten correlation functions in terms of branched covers, which leads to the string theory description. We first observe that the decomposition of the pure Yang-Mills aligns perfectly with decomposition of S_n Dijkgraaf-Witten theory, and then discuss decomposition and the branched covers interpretation. We encounter two puzzles, and to solve them, propose that the Gross-Taylor string theory has a higher-form symmetry.

We will discuss how amplitudes can be used to efficiently derive classical gravitational-wave observables characterizing black hole binary encounters. This technique is very flexible and can be applied to General Relativity, but also to its extensions and, in the spirit of Effective Field Theory, can be used to describe compact objects beyond Schwarzschild black holes. We will briefly discuss some recent applications to spinning black holes and to the subleading Post-Minkowsian waveforms.

The Symmetry Topological field theory (SymTFT) has played an important role in recent studies of symmetries in physics. As one application, it provides a clear and unifying picture of bosonization and fermionization in two dimensions. On the other hand, for theories having a non-anomalous Z_N symmetry with N > 2, people have long speculated about the presence of parafermions. In this informal talk, we revisit the bosonization/parafermionization procedure from the SymTFT point of view, and explain some subtleties and peculiarities involved. It will be based on 2309.01913 and (hopefully) accessible to a broad audience. Part of the London TQFT journal club (https://www.london-tqft.co.uk)

Characters of representations of chiral algebras are important tools in conformal field theory. They are a special chase of chiral torus 1-point functions (namely those where the vacuum has been inserted) and their modular properties famously give rise to the Verlinde formula. In this talk we will generalise from vacuum insertions to insertions from any irreducible representation in the example of the su2 WZW models at non-negative integral level and explore their modular properties.

We will give an intuitive explanation of why and how matrices (or, more precisely, large-N gauge theories) can describe a black hole, without assuming knowledge of quantum mechanics and holographic duality. Firstly, we explain an intuitive picture inroduced by Witten: diagonal entries of matrices describe particles and off-diagonal entries describe strings connecting particles. When many strings are excited, a lot of energy and entropy are packed in a small region and form black hole. Next, we consider classical dynamics of matrix model. Specifically, we colide two black holes. Using the energy conservation, equipartition law of energy and elementary school math, we show that black hole becomes colder after the merger. Matrices know black hole's negative heat capacity! To gain a little bit more intuition, we will look at ants. Collective behavior of ants has a striking similarity to black hole. The mapping rule is ant -> particle, pheromone -> string, and ant trail -> black hole. Tuning parameters such as temperature or each ant's laziness, we can obtain three kinds of phase diagrams. Each of them has a counterpart in large-N gauge theories. If time permits, I will explain the mechanism applicable to strongly-coupled and highly quantum regime needed for quantitative agreement with Einstein gravity. (This part requires a good understanding of undergraduate-level quantum mechanics.)

I will describe some recent developments in applying amplitude and effective field theory ideas in cosmology, and focus in particular on what cosmological measurements (of e.g. the cosmic microwave background or large-scale structure of galaxies) can tell us about the underlying fundamental field theory.

We consider the renormalization group flow of a quantum field theory (QFT) in Anti-de Sitter (AdS) space. We derive sum rules that express UV data and the energy of a chosen eigenstate in terms of the spectral densities and certain correlation functions of the theory. In two dimensions, this leads to a bootstrap setup that involves the UV central charge and may allow us to follow a Renormalization Group (RG) flow non-perturbatively by continuously varying the AdS radius. Along the way, we establish the convergence properties of the newly discovered local block decomposition, which applies to three-point functions involving one bulk and two boundary operators.

Higher-spin theory and massive gauge invariance can be used as input for constraining root-Kerr and Kerr amplitudes, relevant for calculating gravitational observables with spin. Elegant three-point spin-s amplitudes exist for Kerr black holes, however constructing the corresponding four-point Compton amplitudes is an open problem. In this talk, I will discuss the origin of the Kerr three-point amplitudes from a higher-spin theory perspective. Guided by higher-spin constraints and classical-limit analysis, I will propose quantum and classical tree-level Compton amplitudes relevant for root-Kerr and Kerr to all orders in spin.

I will discuss recent work on the numerical conformal bootstrap that modifies the scope of the so-called truncation methods and improves their efficiency. I will show how the proposed approach performs in the recently discussed context of bootstrability for 1d defect CFTs on 1/2 BPS Wilson lines in 4d N=4 SYM theory, how it compares with the more standard linear functional method and how different algorithms allow us to tackle the large-scale non-convex optimization problems that are involved in this method. Along the way, I will address the prospects of AI and Machine Learning in this particular direction.

Recently, a relation was introduced connecting codes of various types with the space of abelian (Narain) 2d CFTs. We extend this relation to provide holographic description of code CFTs in terms of abelian Chern-Simons theory in the bulk. For codes over the alphabet Z_p corresponding bulk theory is, schematically, U(1)_p times U(1)_{-p} where p stands for the level. Furthermore, CFT partition function averaged over all code theories for the codes of a given type is holographically given by the Chern-Simons partition function summed over all possible 3d geometries. This provides an explicit and controllable example of holographic correspondence where a finite ensemble of CFTs is dual to "topological/CS gravity" in the bulk. The parameter p controls the size of the ensemble and "how topological" the bulk theory is. Say, for p=1 any given Narain CFT is described holographically in terms of U(1)_1^n times U(1)_{-1}^n Chern-Simons, which does not distinguish between different 3d geometries (and hence can be evaluated on any of them). When p approaches infinity, the ensemble of code theories covers the whole Narain moduli space with the bulk theory becoming "U(1)-gravity" proposed by Maloney-Witten and Afkhami-Jeddi et al.

We consider gluons scattering in Type IIB string theory on AdS5 x S^5/Z2 in the presence of D7 branes, which is dual to the flavor multiplet correlator in a certain 4d N=2 USp(2N) gauge theory with SO(8) flavor symmetry. We compute this holographic correlator in the large N and finite string coupling tau expansion using constraints from derivatives of the mass deformed sphere free energy, which we compute to all orders in 1/N and finite tau using localization. In particular, we fix the F^4 correction to gluon scattering on AdS in terms of Jacobi theta functions, and the D^2F^4 correction in terms of a non-holomorphic Eisenstein series. At weak string coupling, we find that the AdS correlator takes a remarkably similar form as the flat space Veneziano amplitude. Finally, we combine the numerical conformal bootstrap with the localization constraints to study the correlator at finite N and tau.

I will show that self-dual gravity in Euclidean four-dimensional Anti-de Sitter space (AdS4 ) can be described by a minimally coupled scalar field with a cubic interaction written in terms of a deformed Poisson bracket, providing a remarkably simple generalisation of the Plebanski action for self-dual gravity in flat space. This implies a novel symmetry algebra in self-dual gravity, notably an AdS4 version of the so-called kinematic algebra. This provides a concrete starting point for defining the double copy for Einstein gravity in AdS4 by expanding around the self-dual sector. Moreover, I will show that the new kinematic Lie algebra can be lifted to a deformed version of the w1+∞ algebra, which plays a prominent role in celestial holography.