Abstract
In this talk, I show a construction of transfer matrices for long range spin chains. These transfer matrices define a large set of conserved charges for every length of the spin chain. These charges agree with the original definition of long range spin chains for infinite length. However, this new construction works for every length, providing the definition of integrable finite size long range spin chains. The properties of these finite size Hamiltonians are similar as expected from the wrapping corrections of the planar N=4 super Yang-Mills.

Abstract
One-dimensional protected sectors in the 4d N=4 SYM with a half-BPS boundary or interface are controlled by associative algebras that include U(g) (universal enveloping algebra), W(g,e) (fintie W-algebra), their quantum Hamiltonian reductions, and the Yangian. One can use algebraic techniques and integrability (in the Yangian case) to solve for the correlation functions. The Yangian is found on the interface engineered by a stack of n fivebranes (D5 or NS5), which is related to the inhomogeneous sl_n spin chain. In particular, when n=2, we leverage connection to the inhomogeneous XXX spin chain to compute correlators quite explicitly. Based on 2009.11197 and 2009.11198.

Abstract
Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related model of branched polymers retains these features in any d. I will present a recent theory, developed jointly with A. Kaviraj and E. Trevisani, which aims to explain these facts.

Abstract
BPS invariants of certain physical theories correspond to Donaldson-Thomas (DT) invariants of an associated Calabi-Yau geometry. BPS structures refer to the data of the DT invariants together with their wall-crossing structure. On the same Calabi-Yau geometry another set of invariants are the Gromov-Witten (GW) invariants. These are organized in the GW potential, which is an asymptotic series in a formal parameter and can be obtained from topological string theory. A further asymptotic series in two parameters is obtained from refined topological string theory which contains the Nekrasov-Shatashvili (NS) limit when one of the two parameters is sent to zero. I will discuss in the case of the resolved conifold how all these asymptotic series lead to difference equations which admit analytic solutions in the expansion parameters. A detailed study of Borel resummation allows one to identify these solutions as Borel sums in a distinguished region in parameter space. The Stokes jumps between different Borel sums encode the BPS invariants of the underlying geometry and are captured in turn by another set of difference equations. I will further show how the Borel analysis of the NS limit connects to the exact WKB study of quantum curves. This is based on various joint works with Lotte Hollands, Arpan Saha, Iván Tulli and Jörg Teschner.

Abstract
In this talk, I will present two types of variations of soft theorems. The first one is a soft photon theorem in the near horizon region of Schwarzschild black hole. The second one is a TTbar deformed soft graviton theorem.

Abstract
Gravitational solutions involving shockwaves have attracted significant recent interest in the context of black holes and quantum chaos. Certain classes of supersymmetric two-charge black hole microstates are described by supergravity solutions containing shockwaves, that are horizonless and smooth away from the shockwave. These configurations have been used to describe how black hole microstates absorb and scramble perturbations. In this paper we construct the first family of asymptotically flat supersymmetric three-charge microstate solutions that contain shockwaves. We identify a family of holographically dual states of the D1-D5 CFT and show that these pass a set of tests, including a precision holographic test. We find precise agreement between gravity and CFT. Our results may prove useful for constructing more general families of black hole microstate solutions.

Abstract
I will present an exact formula for the thermal scalar two-point function in four-dimensional holographic conformal field theories. The problem of finding it reduces to the analysis of the wave equation on the AdS-Schwarzschild background. The two-point function is computed from the connection coefficients of the Heun equation, which can be expressed in terms of the Nekrasov-Shatashvili partition function of an SU(2) supersymmetric gauge theory with four fundamental hypermultiplets. At large spin the instanton expansion of the thermal two-point function directly maps to the light-cone bootstrap analysis of the heavy-light four-point function. Using this connection, we obtain the OPE data of heavy-light double-twist operators directly from instanton counting in the SU(2) gauge theory.

Abstract
In this talk we combine integrability and conformal bootstrap to learn about correlation functions of planar maximally supersymmetric Yang- Mills theory. Focusing on correlators of four stress-tensor multiplets, we first introduce a set of dispersive sum rules that are only sensitive to single-traces in the OPE expansion (this is advantageous because this data is available from integrability). We then construct combinations of the sum rules which determine one-loop correlators. Further, we discuss how to employ the sum rules in numerical bootstrap to nonperturbatively bound planar OPE coefficients. As an example, we show a nontrivial upper bound on the OPE coefficient of the Konishi operator outside the perturbative regime.

Abstract
A common method to prepare states in AdS/CFT is to perform the Euclidean path integral with sources turned on for single-trace operators. These states can be interpreted as coherent states of the bulk quantum theory associated to Lorentzian initial data on a Cauchy slice. In this talk, I will first discuss the extent to which arbitrary initial data can be obtained in this way. I will show that the initial data must be analytic and define the subset of it that can be prepared by imposing bulk regularity. Turning this around, I will show that for generic analytic initial data the corresponding Euclidean section contains singularities coming from delta function sources in the bulk. Time permitted, I will discuss an application of these states: I will argue that they provide a way to localize information in perturbative quantum gravity.

Abstract
In supersymmetric theories, global symmetries are encoded geometrically as isometry groups of moduli spaces of vacua. A natural question is therefore whether generalised symmetries such as higher-form and higher-group symmetries understood in a similar manner. I will introduce a refinement of the moduli space of vacua that captures the existence of topological sectors in the infrared and come equipped with actions of generalised symmetries. This will be explored in the context of Higgs and Coulomb branches of 3d N = 4 supersymmetric gauge theories.

Abstract
We discuss a one-parameter family of composite fields which generalise the TTbar operator to arbitrary spacetime dimensions. We show that they induce a deformation of the classical action, which is dynamically equivalent to a field-dependent modification of the metric according to a specific flow equation. We consider a family of abelian gauge theories as particular examples in d = 4. For such models, we obtain the exact expression of the deformed metric. These results imply that the recently proposed Modified Maxwell (ModMax) theory in a specific curved space is dynamically equivalent to its Born-Infeld-like extension in flat spacetime. We also discuss a dimensional reduction of the latter systems from d=4 to d=2 in which an interesting marginal deformation (the so-called root-TTbar deformation) of d=2 field theories emerges.

Abstract
Three dimensional quantum electrodynamics (QED3) coupled to fermions is expected to have a critical flavor number of fermions, which separates the conformal phase from the chiral symmetry breaking phase in the infrared limit. The critical flavor number has been extensively studied in the past decades without a conclusive answer. In this talk, I will show that the conformal bootstrap can shed new light for this long-standing problem.

I will firstly show that the widely interested SO(5)/O(4) symmetric deconfined quantum critical points are just below a new family of kinks in the SO(N) vector bootstrap bounds, while the lattice and perturbative estimates of the critical indices can be excluded by the bootstrap bounds associated with few reasonable assumptions on the spectrum. Then I will explain a remarkable algebraic structure in the bootstrap crossing equations and its fundamental role in bootstrap studies. I will show that the bootstrap bounds are nearly saturated by conformal QED3 after introducing assumptions relevant to conformal QED3. In particular the CFT data of four flavor QED3 can be isolated into a closed region and the bootstrap bounds are beautifully consistent with some large Nf perturbative results. The bootstrap results suggest the critical flavor number of QED3 is slightly above 2 while below 4. I will discuss some predictions and new problems that arose in bootstrap studies.

Abstract
We study Chern-Simons theories at large N with either bosonic or fermionic matter in the fundamental representation. The most fundamental operators in these theories are mesonic line operators, the simplest example being Wilson lines ending on fundamentals. We classify the conformal line operators along an arbitrary smooth path as well as the spectrum of conformal dimensions and transverse spins of their boundary operators at finite 't Hooft coupling. These line operators are shown to satisfy first-order chiral evolution equations, in which a smooth variation of the path is given by a factorized product of two line operators. We argue that this equation together with the spectrum of boundary operators are sufficient to uniquely determine the expectation values of these operators. We demonstrate this by bootstrapping the two-point function of the displacement operator on a straight line. We show that the line operators in the theory of bosons and the theory of fermions satisfy the same evolution equation and have the same spectrum of boundary operators.

Abstract
I will express the torus partition function of a massive integrable QFT with diagonal scattering in terms of a grand canonical ensemble of loops on the torus. The loops interact through scattering factors associated with their intersections. By a Hubbard-Stratonovich transformation, the pairwise interaction of the loops can be decoupled and the partition function expressed as certain expectation value in the Fock space of the Hubbard-Stratonovich auxiliary fields. In the limit where one of the periods of the torus becomes asymptotically large, the H-S fields freeze to their expectation values which are determined by the TBA equation. Based on arXiv.2205.0335

Abstract
We introduce the so-called dual unitary circuits. They are exactly solvable dynamical systems, which are defined on a 1+1 dimensional discrete space time. The defining property of the systems is that they have unitary time evolution, therefore they are good quantum mechanical models, and they also have a unitary evolution operator which translates them along the space direction. These unique properties make them exactly solvable. The models can show integrable and chaotic behaviour as well. In the chaotic cases they present one of the few exactly solvable models, where correlation functions can be computed.

Abstract
I will discuss a class of matrix integrals over the unitary group U(N) with an infinite set of couplings, which include the partition functions of free four-dimensional gauge theories on S3 and the superconformal index of super Yang-Mills theory.

I will show how any such model can be expressed in terms of a system of free fermions in an ensemble parameterized by the infinite set of couplings. Integrating out the fermions in a given quantum state leads to a convergent expansion as a series of determinants. By further averaging over the ensemble, we obtain a formula for the matrix integral as a q-series with successive terms suppressed by q^N. This provides a matrix-model explanation of the giant graviton expansion that has been observed recently in the literature.

Abstract
In this talk, I will talk about two tales of TTbar deformation. The first one regards explicitly supersymmetric TTbar deformations of N=1 and N=2 supersymmetric quantum mechanics. Written in terms of Noether currents associated with translations in superspace, these deformations are on-shell equivalent to the dimensionally reduced supercurrent-squared deformations of 2d N=(0,1) and N=(1,1) theories, respectively. In the N=1 case, two forms of the deformation driving the same flow are presented. Another tale is on TTbar deforming the 1d dual to the 2d BF formulation of JT gravity, where fundamental observables are Wilson lines and loops. After interpreting this deformation as a modification of the BF theory boundary condition, we study the deformed correlators of boundary-anchored Wilson lines in the 3d Chern-Simons lift of BF theory. Analogous correlators in BF theory per se are also calculated below the Hagedorn temperature, where the SL(2,R) principal series dominates over the discrete series. This talk is based on joint work arXiv:2204.05897 and arXiv:2205.07817 with S. Ebert, C. Ferko, and Z. Sun.

Abstract
I will review various aspects of 3d N=4 gauge theories on a closed Riemann surface. In particular, I will discuss the twisted indices of these theories and their geometric interpretations. I will also comment on the explicit construction of the twisted Hilbert spaces of these theories.

Abstract
Crosscap states have been studied extensively in two-dimensional conformal field theory in the past, where part of the motivations came from their connection to orientifolds in string theory. Surprisingly however, analogous studies in (massive) integrable theories have been lacking. In this talk, I will fill this gap by presenting a systematic study of crosscap states in integrable field theories and spin chains. First, I derive an exact formula for overlaps between the crosscap state and any excited state in integrable field theories with diagonal scattering. Using the formula, I compute the crosscap entropy i.e. the overlap with the ground state in several examples, and find that it decreases monotonically along the renormalization group flow except in cases where the discrete symmetry is spontaneously broken in the infrared. We next introduce crosscap states in integrable spin chains and obtain exact determinant expressions for overlaps with energy eigenstates. These states are long-range entangled and provide interesting initial conditions for the quantum quench protocol, which are quite distinct from short-range entangled states corresponding to the boundary states.

Abstract
Black hole information paradox is a well known problem and significant progress was made recently. In particular the island formula for the radiation entropy gives Page curve and therefore maintains unitarity. In this talk I will discuss how to derive Page curve from holography. We provide an explicit construction of gravity system attached with bath based on partial reduction. We compute both entanglement entropy and reflected entropy, and find that they precisely agree with island formula.

Abstract
In this talk I will describe toy models of holography for non-AdS spacetimes that are obtained by deforming the bulk and boundary sides of the AdS3/CFT2 correspondence. In the bulk we consider string theory on AdS3 supported by NS-NS flux and perform a marginal deformation of the worldsheet action by the antisymmetric product of two Noether currents. We show that such marginal deformations are equivalent to TsT transformations of the background geometry. Depending on the choice of these currents we can obtain asymptotically flat or asymptotically warped AdS spacetimes. On the boundary side, these deformations have been argued to correspond to single-trace irrelevant deformations of two-dimensional CFTs that include the TTbar, JTbar, TJbar deformations or any linear combinations of them. We check that the perturbative spectrum of strings on the TsT-transformed backgrounds, the thermodynamics of black holes, and properties of the ground state geometry match those of the boundary theories.

Abstract
Entanglement island is the recently emergent concept in quantum gravity. It plays an essential role in resolving the black hole information paradox. However, existing calculable models of entanglement islands are mainly in two dimensional toy models of quantum gravity for which there are no local graviton modes. In order to search for entanglement island and study its properties in higher dimensions, we will use the Karch-Randall braneworld. This theory is doubly holographic and we can perform explicit calculations locating the entanglement islands using holography. We will formulate a version of the black hole information paradox in the Karch-Randall braneworld and see how entanglement island helps us to resolve this paradox. Our calculation is performed in a simple case of Karch-Randall braneworld and it is purely analytic. Interestingly, the gravitational theory localized on the Karch-Randall brane is massive and this is due to the fact that the brane is coupled to a bath which violates the energy-momentum conservation on the brane and the mass of the graviton is therefore a one-loop quantum effect. Based on this observation, we will formulate a conjecture that entanglement islands exist only in massive gravity theories. If time is allowed we will briefly discuss our further study of this conjecture and the proof of it in a large class of spacetimes including asymptotically anti-de Sitter spacetimes.

Abstract
The notion of integrability for classical (field) theories has been almost entirely studied from the Hamiltonian point of view since the early days of the modern theory of integrable systems. In 2009, the notion of Lagrangian multiform was first put forward by Lobb and Nijhoff as a purely Lagrangian framework to capture integrability. The main idea is to formulate a generalised variational principle for an action involving a certain differential form whose coefficients are interpreted as Lagrangians for a hierarchy. Since its proposal, this idea has flourished in various directions and I will review the main developments for classical field theories in 1+1 dimensions.

Two key ingredients are the multiform Euler-Lagrange equations and the so-called closure relation, both of which derive from the generalised variational principle. In this talk, I will present the connection between Lagrangian multiform theory and the well-established theory of the classical r-matrix which had a purely Hamiltonian interpretation so far. I will explain how the classical Yang-Baxter equation underpins the fundamental properties of a certain Lagrangian multiform and the corresponding zero curvature equations. A large variety of known hierarchies are contained as special cases, such as the Ablowitz-Kaup-Newell-Segur hierarchy, the sine-Gordon (sG) hierarchy and various hierarchies related to Zakharov-Mikhailov type models which contain the Faddeev-Reshetikhin (FR) model and recently introduced deformed sigma/Gross-Neveu models as particular cases.

Time permitting, I will also illustrate the versatility of our method by showing how to construct new examples of integrable field theories and their hierarchies by coupling integrable hierarchies together. We provide two examples: the coupling of the nonlinear Schrödinger system to the FR model and the coupling of sG with the anisotropic FR model.

This most recent results are based on the joint work arXiv:2201.08286 with M. Stoppato and B. Vicedo.

Abstract
I will speak about my recent work with Zechuan Zheng where we study the SU(N c) lattice Yang-Mills theory in the ’t Hooft limit N → infinity, at dimensions D=2,3,4, via the numerical boot strap method. It combines the Makeenko-Migdal loop equations, with the cut-off L on maximal length of loops, and the positivity conditions on certain correlation matrices. Our algorithm is inspired by the pioneering paper of P.Anderson and M.Kruczenski but it is significantly more efficient, as it takes into account the symmetries of the lattice theory and uses the relaxation procedure in the line with our previous work on matrix bootstrap. We thus obtain the rigorous upper and lower bounds on plaquette average at various couplings and dimensions. The results are quickly improving with the increase of cutoff L. For D=4 and L=16, the lower bound data appear to be close to the Monte Carlo data in the strong coupling phase and the upper bound data in the weak coupling phase reproduce well the 3-loop perturbation theory. We attempt to extract the information about the gluon condensate from this data. Our results suggest that this bootstrap approach can provide a tangible alternative to, so far uncontested, Monte Carlo approach. I will also mention our results on the bootstrap approach for an unsolvable two-matrix model in the large N limit. Matrix bootstrap appears to be superior in efficient over Monte Carlo.

Abstract
AdS/CFT provides a consistent non-perturbative definition of quantum gravity in asymptotically AdS spacetimes. Black holes should correspond to ensembles of states in the boundary field theory. By performing a careful analysis of the superconformal index of 4d N=4 SU(N) Super-Yang-Mills theory, with the help of a Bethe Ansatz type formula that I will review, we are able to exactly reproduce the Bekenstein-Hawking entropy of BPS black holes in AdS5 x S5. The large N limit exhibits many competing contributions, that we are able to identify with complex saddles of the (putative) gravitational path-integral. Along the way we propose a necessary condition for complex saddles to contribute, based on the size of their non-perturbative corrections. Such a prescription reproduces the field theory analysis. Yet, field theory seems to predict undiscovered gravitational solutions.

Abstract
Off-central heavy ion collisions have produced a strong magnetic field. The quark-gluon plasma in strong magnetic field is known to have distinct transport properties. In this talk, I will discuss the magneto-vortical effect, which is closely tied to chiral anomaly and can be viewed both as the celebrated chiral magnetic and chiral vortical effect. I will discuss studies of the magneto-vortical effect in strongly coupled QGP using holographic method and also weakly coupled QGP using chiral kinetic theory. I will also discuss matching with general framework of magnetohydrodynamics.

Abstract
I will review the countings of BPS invariants via exponential/spectral networks and present an interpretation of this counting as a count of certain points in the moduli space of A-branes corresponding to degenerate Lagrangians.

Abstract
Reformulating symmetries as a subsector of quasi-topological defects of various codimensions generalizes the notion of symmetry group to a symmetry fusion algebra (or a categorical symmetry). Sometimes, such fusion algebras organize nicely in 2-group structures. 2-group symmetries are ubiquitous in the landscape of field theories: these have been found in simple theories such as QED, as well as in some of the most exotic like 6d little strings. In this seminar we will discuss some applications of geometric engineering techniques in M-theory to unravel these structures for theories without a Lagrangian formulation.

Abstract
We consider limits of N = 4 super-Yang-Mills (SYM) theory that approach BPS bounds. These limits result in non-relativistic theories that describe the effective dynamics near the BPS bounds and upon quantization are known as Spin Matrix Theories. The near-BPS theories can be obtained by reducing N = 4 SYM on a three-sphere and integrating out the fields that become non-dynamical in the limits. I will present various subsectors including PSU(1,1|2) and SU(1,2|2) types of subsectors in this limit. We finally analyse the symmetry structure of the sectors in view of an interpretation of the interactions in terms of fundamental blocks. This is based on two publications: 2012.08532 and 2111.10149, and one work in progress.

Abstract
I will present a preliminary result on the third-order correction in 1/N expansion to the four-point correlator of the stress tensor multiplet in N=4 super Yang--Mills theory at large 't Hooft coupling, which corresponds to the two-loop scattering of four gravitons in the dual AdS5×S5 supergravity. This is obtained by bootstrapping an educated ansatz based on intuitions from the hidden 10-dimensionthe conformal symmetry, which I will describe in detail.

Abstract
In this talk, I will talk about the phenomena of eigenstate thermalization in the context of 2d CFT. I shall discuss its relation to and derivation of the appearance of forbidden singularities in Virasoro blocks in the thermodynamic limit. Beyond that I will discuss the resolution of these singularities by finite effects, in the form of zero-condensations in Virasoro block.

Abstract
We introduce and analyze tetrahedron instantons, which can be realized in string theory by D0-branes probing a configuration of intersecting D6-branes with a nonzero constant background B-field. Physically they capture instantons in six-dimensional gauge theories with the most general intersecting codimention-two supersymmetric defects. We study the properties of the moduli space of tetrahedron instantons. We compute the instanton partition function, which lies between the higher-rank Donaldson-Thomas invariants and the partition function of the magnificent four model. Remarkably the instanton partition function has a closed-form expression in terms of the plethystic exponential, and matches the index of M-theory on a Calabi-Yau fivefold. Our computations provide an equivariant test of the duality between M-theory and type IIA string theory.

Abstract
In this seminar I will discuss the content of the papers I presented in the year 2021. The main message is a method to write holographic duals to super-conformal field theories in dimensions D=1,2,3,4,5,6. Various checks of the dualities will be presented and some recent predictions will be discussed. I will try to make the material accessible to graduate students, postdocs and faculty, not necessarily working on these topics. There is a final part more directed to the string theorists working on these themes.

Abstract
Recent studies of scattering amplitudes reveal an intrigue duality between color and kinematics. This color-kinematics (CK) duality also indicates a deep connection between gauge and gravity theories via the so-called double copy. In this talk, I will first give an introduction to the CK duality and the double-copy picture, then I will discuss some new progress on the high-loop CK-dual solutions and the double-copy prescription for form factors.