Abstract
In this talk, I will talk about my recent researches about how to apply the idea of holography into the models with global SU(1,d) kind of symmetry. I will provide some examples of this possibility. One is about Spin Matrix theory, which is defined as the non-relativistic limit of four-dimensional N=4 SYM. I will show our construction obeys the global PSU(1,2|3) symmetry. In the second example, I will show some recent work in understanding SU(1,2) type of gravitational models.

Abstract
We study regularization scheme dependence of Kaehler (N=2) supersymmetric sigma models. At the one-loop order, the metric beta-function is the same as in the non-supersymmetric case and coincides with the Ricci tensor. First correction in the MS scheme is known to appear at the fourth loop (Grisaru et al., 1986). We show that for certain integrable Kaehler backgrounds, such as complete T-dual of eta-deformed CP(n) sigma models, there is a scheme in which the fourth loop contribution vanishes.

Abstract
Even when the bulk theory is conformal (or quasi-conformal), external probes (defects) may undergo a nontrivial RG flow. In this talk, I will briefly review some general properties of line defects in CFT. I will then discuss some interesting RG flows for Wilson lines in massless gauge theories and their relation with an instability to screening by charged fields.

Abstract
Entanglement contour and Rényi contour reflect the real-space distribution of entanglement entropy, serving as the fine structure of entanglement. In this talk, we will introduce our recent work on unraveling the hyperfine structure by rigorously decomposing Rényi contour into the contributions from particle-number cumulants. We show that the hyperfine structure, introduced as a quantum-information concept, has several properties, such as additivity, normalization, symmetry, and unitary invariance. To extract the underlying physics of the hyperfine structure, we numerically study lattice fermion models with mass gap, critical point, and Fermi surface, and observe that different behaviors appear in the contributions from higher-order particle-number cumulants. We also identify exotic scaling behaviors in the case of mass gap with nontrivial topology, signaling the existence of topological edge states. In conformal field theory (CFT), we derive the dominant hyperfine structure of both Rényi entropy and refined Rényi entropy. By employing the AdS3/CFT2 correspondence, we find that the refined Rényi contour can be holographically obtained by slicing the bulk extremal surfaces. The extremal surfaces extend outside the entanglement wedge of the corresponding extremal surface for entanglement entropy, which provides a new tool to probe the hyperfine structure of the subregion-subregion duality in the entanglement wedge reconstruction.

Abstract
The space of 4d quantum field theories (QFTs) can be thought of as the Renormalization Group flows between Conformal Field Theories (CFTs). The a-theorem tells us that CFTs can be ordered by their a-anomaly value. I will explain how one can use the (numerical) S-matrix bootstrap methods to search for the minimal allowed value of the a-anomaly. I will also mention ongoing work to access the c-anomaly using probe gravitons.

Abstract
3d mirror symmetry for theories with eight supercharges is understood in terms of Hanany-Witten brane setups and plays an important role in many areas of supersymmetric qft’s. The generalization to theories with four supercharges, in the non-Abelian case, has not been understood so far. In this talk, based on work in progress with Riccardo Comi and Sara Pasquetti, we focus on brane setups with NS and D5’ branes, proposing that the related quiver gauge theories involve ‘generalized bifundamentals’, that is strongly coupled qft’s which are ancestors of the well known T[SU(N)] theories. Our proposal leads to 3d mirror dualities that can be exactly proven, reducing them to known Seiberg-like dualities. This gives strong support to the proposal. The simplest example is the duality between adjoint SQCD with F flavors, and a generalized quiver with F-1 nodes and F-2 generalized bifundamentals.

Abstract
After reviewing quantum mechanics monopoles, I will describe how holography, localization and integrability yield non-perturbative data on ’t Hooft loops in the N=4 Super-Yang-Mills theory.

Abstract
In this talk, I would like to report our recent work arxiv: 2301.07957. We computed the conformal blocks with one irregular operator in the Liouville theory using the Coloumb Gas method, also known as the free field integral representation. We derived the relation of monodromies and Stokes matrices of these conformal blocks as well as the braiding representations. Along the way, I would explain the related mathematical terms using simple examples. I may talk about possible applications of our results if time permits.

Abstract
I will review our recent work on counting BPS states in superconformal quantum mechanics. The main application is providing evidence for a holographic duality between certain SCQM models and Ultra-Spinning supersymmetric black holes in AdS. Our work also leads to new results characterizing the asymptotic growth of the dimensions of the cohomology of the ADHM moduli space of Yang-Mills instantons.

Abstract
In this talk, I will demonstrate how discrete cluster integrable systems can provide a comprehensive understanding of the stable BPS particle spectrum in five-dimensional theories on a circle. These theories emerge from the geometric engineering of M-theory on toric Calabi-Yau threefolds. While their BPS spectrum is typically wild, with an infinite number of states of arbitrarily high spin, specific algebraic solutions of the integrable systems indicate the existence of tame chambers, associated with gauge theory phases. In these chambers, the BPS spectrum can be expressed in closed form and comprises vector multiplets, infinite towers of hypermultiplets, and Kaluza-Klein states. By utilizing wall-crossing formulas, it becomes possible to obtain the spectrum in any other chamber. To illustrate this methodology, I will examine the concrete example of local del Pezzo threefolds, geometrically engineering SU(2) Super Yang-Mills with matter, and their corresponding q-Painleve' cluster integrable system. Additionally, time permitting, I will briefly discuss the interpretation of the aforementioned results through the lens of WKB approximation for q-difference equations.

Abstract
We propose a dual Wilson loop description for the MHV super form factors of half-BPS operators in planar N = 4 super-Yang-Mills theory. In this description, the local operators are represented by on-shell states, made out of zero-momentum particles, that are absorbed by a null periodic super Wilson loop. We present evidence for this duality at weak coupling, by performing an explicit calculation of the Wilson loop matrix elements through one loop. At tree level, the interactions localize at the cusps of the loop, revealing a simple connection between the super form factors and the m = 2 tree amplituhedron. At loop level, we show that the Wilson loop calculation reproduces the known results for the super form factors. Inspired by this duality, we extend the OPE program developed for the form factors of the Lagrangian to the super form factors of the higher-charge operators. We introduce non-perturbative axioms and conjectures for the main building blocks that govern the exchange of the lightest flux-tube excitations. These blocks appear as simple refinements of the form factor transitions introduced in earlier OPE studies. They are expressed at any value of the ’t Hooft coupling in terms of the tilted Beisert-Eden-Staudacher kernel. We carry out checks of our conjectures up to two loops at weak coupling for three- and four-point form factors of half-BPS operators of various lengths, finding perfect agreement with perturbative data.

Abstract
In this talk, I will show that the large charge sector of the SU(2) N=4 SYM provides a solvable corner of the theory which exhibits striking similarities with the standard planar limit. In particular, I will describe how to compute the spectrum of local operators and higher point correlation functions involving two large charge operators and several light operators.

Abstract
In this talk I will review the ultimate goals and limitations of conformal bootstrap methods. In particular, I will argue that to reach the bootstrap endgame, it is crucial to work with improved tools for analyzing bootstrap equations. I will argue that a complete set of such tools is now available for solving 1d CFTs: they are essentially versions of Fourier transform for bootstrap equations known as extremal functionals. I explain why these significantly outperform traditional bootstrap methods and how they can be used for large scale numerical, as well as analytic applications.

Abstract
A large class of the theories of M2-branes can be constructed by the type IIB brane setups of Hanany-Witten type. The partition function of these theories enjoys discrete symmetries, part of which can be understood as the IR dualities associated with the Hanany-Witten transitions. The symmetries become manifest under the equivalence between the partition functions and the quantization problem of one-dimensional curves (Fermi gas formalism), where the symmetries are the coordinate transformations of the associated curves. In particular, when the symmetry is an exceptional Weyl group, it suggests that the partition function solves a non-linear integrable system called q-discrete Painlevé equation associated with the Weyl group. We demonstrate this explicitly for the case where the symmetry is E5 (= SO(10)) Weyl group, finding novel identities among the partition functions at different ranks of the gauge groups and other parameters.

Abstract
4d N=2 SCFTs of class S are associated with punctured Riemann surfaces. Sometimes, theories associated with different punctured Riemann surfaces appear to describe the same physics -- at least insofar as we can compare physical properties such as the central charges, flavor symmetry algebra/group, the spectrum of Coulomb branch operators, and the Schur and Hall--Littlewood indices. I will show whether such a pair of seemingly-dual theories are, in fact, dual by considering their uplift to 6d (1,0) SCFTs. Using the tensor branch effective field theory description, we can answer whether two 6d (1,0) SCFTs are isomorphic, and thus whether the class S descriptions of the torus-compactifications are truly dual.

Abstract
I will discuss a recently introduced approach to the study of non-protected observables in N=4 SYM. The idea - dubbed Bootstrability - is to combine exact information from Integrability (which for us will mean data on the spectrum) with the constraints of the Conformal Bootstrap. Integrability data on the spectrum help to focus on a point in theory space and lead to much narrower bounds for the OPE coefficients. I will describe the first applications of this idea in the case of the line defect CFT living on a supersymmetric Wilson line in the 4D gauge theory. In particular, I describe two different strategies to incorporate information from integrability in the bootstrap - first through data on the spectrum of physical operators, and then through data on deformations, such as the deformation associated with bending the Wilson line to form a cusp. In the last part of the talk, I will discuss ongoing work which includes new bootstrap strategies.

Abstract
Quasiparticles are collective modes in many-body systems that can mimic semiclassical particles under some circumstances. I will talk about the emergence of semiclassical features in quasiparticle states of quantum spin chains using two quantum information quantities, entanglement entropy and subsystem distance. I will also demonstrate how the semiclassical description fails for a different measure, Shannon entropy.

Abstract
Unlike in cases with maximal or half-maximal supersymmetry, the spectrum of supersymmetric black holes in type II string theory compactified on a Calabi-Yau threefold with generic SU(3) holonomy remains partially understood. Mathematically, the BPS indices counting these states coincide by the generalized Donaldson-Thomas invariants associated with the derived category of coherent sheaves, but they are rarely known explicitly. String dualities indicate that suitable generating series of rank 0 Donaldson-Thomas invariants counting D4-D2-D0 bound states should transform as vector-valued mock modular forms, in a very precise sense. I will spell out and test these predictions in the case of one-modulus compact Calabi-Yau manifolds (such as the quintic threefold), where the BPS indices can (at least in principle) be computed from Gopakumar-Vafa invariants, using recent mathematical results by S. Feyzbakhsh and R. Thomas.

Abstract
The discovery of integrability in the context of the AdS/CFT correspondence has led over the last 20 years to a plethora of exact results for physical, non-protected, observables. This gave us the opportunity to explore and test the holographic principle. Remarkably, it is possible to continuously deform the string theory on various AdS backgrounds while preserving this powerful property of integrability, but giving up some manifest symmetries, including supersymmetry. In this talk, I will give an overview of these deformations, including T-duality--shift--T-duality (TsT) transformations, deformed non-abelian T-dualities, and quantum deformations such as the so-called eta- and lambda-deformations. Studying them teaches us lessons about the space of integrable string theories and the robustness of AdS/CFT.

Abstract
In this talk, I will first introduce the construction of generalized complete intersection Calabi-Yau manifold (gCICY), which is a new method of constructing Calabi-Yau manifold. However, I will show that the standard algebraic method to generate new gCICYs is very laborious. Because of this complexity, the number of gCICYs and their classification still remains unknown. Then I will discuss how to make some progress in this direction using neural networks. Our results showed that the trained models can get high accuracy on the type (1, 1) and type (2, 1) gCICYs existing in the literature. Moreover, we can achieve a 97% accuracy in predicting new gCICYs not used in the training.

Abstract
The TsT transformation of string theory on AdS$_3\times {\cal N}$ with NS-NS flux has been conjectured to be holographically dual to a single trace TTbar deformation of the symmetric orbifold CFT on the AdS$_3$ boundary. In this talk, we present a non-perturbative calculation of two-point correlation functions using string theory and demonstrate their consistency with those of the TTbar deformation. At un-twisted sector, the non-perturbative result satisfies the Callan-Symanzik equation for double trace TTbar deformed CFT derived by Cardy. We also perform conformal perturbations on both the worldsheet CFT and the symmetric orbifold CFT as a sanity check. The perturbative and non-perturbative matching between results on the two sides provides further evidence for the conjectured TsT/TTbar correspondence. This talk is based on the joint work with W. Cui, W. Song and J. Wang.

Abstract
I will talk about my recent work 2303.17623 on non-BPS branes in heterotic superstring theories. Their existence is suggested by some topological charges, and we give the exact worldsheet description of the near horizon limits of these branes. This is a collaboration with Kaidi, Ohmori and Tachikawa.

Abstract
We study the N = 4 SYM stress tensor multiplet 4-point function for any value of the complexified coupling tau, and in principle any gauge group (we focus on SU(2) and SU(3) for simplicity). By combining non-perturbative constraints from the numerical bootstrap with two exact constraints from supersymmetric localization, we are able to compute upper bounds on low-lying CFT data (e.g. the Konishi) for any value of tau. These upper bounds are very close to the 4-loop weak coupling predictions in the appropriate regime. We also give preliminary evidence that these upper bounds become small islands under reasonable assumptions, in which case our method would provide a numerical solution to N = 4 SYM for any gauge group and tau.

Abstract
The Quantum Spectral Curve (QSC) is a powerful integrability-based formalism capable of computing the non-perturbative spectrum of planar N=4 SYM. The success and utility of QSC motivate trying to extend it beyond N=4 to other instances of the AdS/CFT correspondence where integrability is expected to be present. Recently, two different groups proposed identical conjectures for a QSC describing planar string theory on AdS3*S3*T4 with pure RR-flux. The conjectures were based on symmetry arguments of the Q-system underlying the QSC construction. I will review the basics of the QSC framework in the well-understood AdS5 case. Thereafter I will explain the conjectured curve and how it differs from previous iterations of the QSC. Furthermore, I will discuss recent perturbative results with a peculiar structure. Hopefully, these results can soon be confirmed, or disproved, by using the recently constructed TBA for AdS3.

Abstract
The study of generalized global symmetries is related to the presence/absence of discrete structures in quantum field theory, e.g. the presence/absence of discrete gauge fields in the theory. In light of this, it is natural to ask if such discrete structures play a role in the celebrated examples of 3d N=4 mirror symmetry. That is, whether the believed 3d N=4 mirror pairs are precisely dual to each other, or rather they are dual only if one mods out extra coupled TQFTs. In this talk, I will discuss a series of recent papers with Mathew Bullimore, Andrea Ferrari, and Sakura Schafer-Nameki, where we probed this problem in a variety of ways, which involved understanding global forms of Higgs branch and (IR enhanced) Coulomb branch symmetries, 1-form symmetries, and ‘t Hooft anomalies of these symmetries. We found all this information matched exactly across mirror pairs involving unitary and special unitary gauge groups, meaning that no discrete modification of mirror symmetry is needed in all these cases! This may be good or bad news, depending on one’s taste; however, in the process we uncovered fundamental conceptual relationships between the study of generalized global symmetries and anomalies on one hand, and the study of various types of monopole operators and associated monopole formulas on the other hand. Another application of our methods is the deduction of generalized symmetries and anomalies of higher-dimensional SCFTs using their magnetic quivers. Based on ArXiv: 2301.02249 and 2205.15330.

Abstract
In this talk, we will present how a Heisenberg spin chain emerges from the two-dimensional N=(2,2) gauge theory at an intermediate scale, which relies on the renormalization group flow guided by the global symmetries and the dynamics of domain walls. Two examples will be discussed: XX-model and its K-theoretic version. Finally, we will briefly comment on the unification of gauge theories from the point of view of the spin chain, and how to approach other formulations of an integrable system via a new point of view.

Abstract
I will introduce recent definitions of the operator growth and state complexity based on the Krylov basis. I will then present various examples and discuss open questions.

Abstract
In this work, we construct several diffeomorphism invariant observables in AdS3 gravity in the context of the entanglement wedge cross section. The set of observables that we construct includes the entanglement wedge cross section and four extra half geodesics' lengths. We try to study the properties of these observables in Hamiltonian formalism, including the system's evolutions generated by these observables and the brackets between these observables. We use two methods to study these questions, by Brown-York tensor’s bracket in covariant phase space formalism and by canonical formalism, which give consistent results. With the two methods, we get several interesting results related to these questions. We find that these observables may generate a novel behavior in the system's evolutions, which include a split somewhere on the Cauchy surface. We compute the brackets between these observables, and the only non-zero ones are the brackets between the entanglement wedge cross section and the half geodesics. Taking use of these brackets in the context of entanglement wedge cross section, we also construct a slightly different geodesic network where all of the geodesics' lengths commute with each other.

Abstract
Applying the recently developed method—the off-diagonal Bethe ansatz method, we construct the exact solutions of the Heisenberg spin chain with various boundary conditions. The results allow us to calculate the boundary energy of the system in the thermodynamic limit. The method used here can be generalized to study the thermodynamic properties and boundary energy of other high-rank models with non-diagonal boundary fields.

Abstract
In the CFT literature, there are two well-known claims: - In any unitary CFT, a twist gap in the spectrum of operator product expansion of identical scalar primary operators (with scaling dimension Δ) implies the existence of a family of primary operators with arbitrarily large spin and twist arbitrarily close to 2Δ. - In any 2d CFT (with Virasoro symmetry, modular invariance, c>1) with a normalizable vacuum and a twist gap in the spectrum of Virasoro primaries, there exists a family of Virasoro primaries with h arbitrarily large and hbar arbitrarily close to (c-1)/24. They are based on some (non-rigorous) CFT arguments which are called the “light-cone bootstrap”. In this talk, I will present a proof of the two claims and some potential generalizations. The talk will be based on [arxiv: 2212.04893].

Abstract
N M5-branes probing the intersection between the orbifold C^2/Zk and an E8 wall give rise to 6d (1,0) SCFTs known as A-type orbi-instantons. At fixed N and k, each element of Hom(Zk,E8) defines a different SCFT. The SCFTs are connected by Higgs branch RG flows. We determine the full hierarchy of these RG flows for any value of N and k. The hierarchy takes the form of an intricate Hasse diagram: each node represents an IR orbi-instanton (homomorphism), and each edge an allowed flow, compatibly with the 6d a-theorem. The partial order is defined via quiver subtraction of the 3d magnetic quivers associated with the 6d SCFTs.