Scientific Programme

**Preliminary Scientific Programme**

The Scientific Programme is available for download here.

**Discussion Session - **Wednesday 21/7/2021 h.11.15

**Vladimir Kazakov ****(presentation)**

**Discussion on AdS/CFT integrability.** After a short (and incomplete) introduction on the current state of AdS/CFT integrability, I will propose the audience to discuss the topics and questions presented in the last two slides. Many of these questions have been proposed to me by a few participants of IGST. You are also welcome to pose your questions on the dedicated Slack workspace of IGST and continue there the discussion as long as it goes.

**Titles and abstracts**

**Benjamin Basso - slides**

**Dressing up the pair of pants in planar N=4 SYM. ** I will talk about the calculation of 3pt functions of single-trace operators in planar N=4 SYM using the hexagon method. The method is well known to encounter difficulties for short operators, with wrapping divergences plaguing the formalism when the two hexagons are tied tightly together. I will recall how to renormalize these divergences away in the simplest situations and explore the resulting pattern of finite-size corrections. In particular, I will unveil a new type of wrapping corrections - the cubic wrapping - with mirror excitations travelling across all three channels of the pair of pants, and use it to resolve a discrepancy with string theory at strong coupling and match gauge theory data at five loops. Lastly, I will present a conjecture for the simplest structure constants that incorporates the infinite tower of wrapping corrections by means of "simple" dressing factors and detail some high-order checks at strong coupling. Based on work in progress with Alessandro Georgoudis.

**Gabriel Bliard - slides**

**Mellin amplitudes and 1D CFTs**. In this talk, I will present the construction of a Mellin transform which is tailored to one dimensional conformal field theories while preserving some of the key properties of its higher dimensional relative. Using this formalism, I will consider perturbations generated by quartic scalar interactions in AdS2 with L derivatives and the first order CFT data of these theories, matching and extending the bootstrap-based results. Finally, I will present the holographic system of a half-BPS Wilson line, where Witten diagrams, analytic bootstrap and superspace methods are used to find the CFT data of the corresponding operator insertions.

**Dmitry Bykov ****- slides**

**Sigma models as Gross-Neveu models.** I will show that there is a wide class of integrable sigma models that are exactly and explicitly equivalent to bosonic Gross-Neveu models. In full generality these are models with quiver variety phase spaces, but the familiar CP^n, Grassmannian or flag manifold sigma models belong to this class as well. This approach leads to a new take on topics such as RG (Ricci) flow, construction of integrable deformations and the inclusion of fermions. In particular, it provides a way of obtaining worldsheet SUSY theories from target space SUSY theories by means of a supersymplectic quotient.

**Andrea Cavaglià ****- slides**

**Integrability and conformal bootstrap for observables beyond the spectrum.** I will describe two very different approaches one may take to compute observables beyond the spectrum in N=4 SYM and related theories. In the first part of the talk, I will consider the Separation of Variables (SoV) philosophy, which suggests that we can find an analytic solution for correlators. I will present recent work with N. Gromov and F. Levkovich-Maslyuk on the fishnet limit of N=4 SYM. Using the method of the functional SoV, we obtain some prototype observables in separated variables, including a special type of 3-point function, and a proposal for a building block of defect 1-point functions. In the second part, I will explore the combination of integrability results with the techniques of the numerical conformal bootstrap to obtain "experimental data" on the theory at finite coupling. This is based on work to appear with N. Gromov, J. Julius and M. Preti, where we consider the one-dimensional defect CFT living on a Maldacena-Wilson line in N=4 SYM. We compute part of the defect spectrum using integrability and, using the constraints of the conformal bootstrap, obtain an accurate determination of an OPE coefficient at any value of the 't Hooft coupling.

**Riccardo Conti ****- slides**

**ODE/IM correspondence in the large momentum limit.** In its original form, the ODE/IM correspondence establishes a link between spectral determinants of certain Ordinary Differential Equations (ODE) and Integrals of Motion of Integrable Models (IM). In the first part of the talk I will briefly introduce the topic from an historical perspective and comment on the current state of the art. In the second part, I will report some of my recent efforts, in collaboration with Davide Masoero, towards the proof of the correspondence for a specific Integrable Model, i.e. quantum Korteweg-de Vries (KdV).

**Pietro Ferrero ****- slides**

**Bootstrapping the 1/2-BPS line defect CFT in N=4 super Yang-Mills. **We consider the 1d CFT defined by the half-BPS Wilson line in planar N = 4 super Yang-Mills. Using analytic bootstrap methods we derive the four-point function of the super-displacement operator at fourth order in a strong coupling expansion. Via AdS/CFT, this corresponds to the first three-loop correlator in AdS ever computed. To do so we address the operator mixing problem by considering a family of auxiliary correlators. We further extract the anomalous dimension of the lightest non-protected operator and find agreement with the integrability-based numerical result of 2001.11039.

**Rouven Frassek ****- slides**

**QQ-system construction of so(2r) spin chains.** I will review the QQ-system and oscillator construction of Q-operators for su(r+1) spin chains and discuss its generalisation to so(2r) spin chains.

**Matthias Gaberdiel ****- slides**

**The string dual of free N=4 SYM. **A proposal for the worldsheet string theory that is dual to free N=4 SYM in 4D will be explained. It is described by a free field sigma model on the twistor space of AdS5 x S5, and is a direct generalisation of the corresponding model for tensionless string theory on AdS3 x S3. I will explain how our proposal fits into the general framework of AdS/CFT, and review the various checks that have been performed. (Based on joint work with Rajesh Gopakumar.)

**Michael Green**

**Exact duality-invariant expression for an integrated correlator in SU(N) N=4 Yang–Mills theory.** This talk will present the exact expression for an integrated correlator of four superconformal primary operators in the stress tensor multiplet of SU(N) N=4 supersymmetric Yang-Mills. This is related to the partition function of the N=2* theory that is determined by supersymmetric localisation. I will show that this integrated correlator can be expressed as a strikingly simple two-dimensional lattice sum. This is a function of the complex Yang–Mills coupling and is manifestly invariant under SL(2,Z) (Montonen–Olive) duality. The correlator satisfies a powerful Laplace equation that relates its value for SU(N) to its value for SU(N − 1) and SU(N + 1). For finite N the correlator reproduces and extends perturbative and non-perturbative N=4 SYM results. The large-N expansion is holographically related to the SL(2,Z)-invariant low energy expansion of the type IIB superstring four-graviton amplitude in AdS5×S5. The talk will also describe the extension of these results to n-point correlators with n>4 that violate the U(1) bonus symmetry maximally.

**Luca Griguolo ****- slides**

**Decoding one-dimensional subsectors in Chern-Simons matter theories.** Three dimensional gauge theories with at least N=4 supersymmetry contain interesting one-dimensional subsectors, sometimes exactly solvable thanks to supersymmetric localization. I will discuss two particular examples in the situation when Chern-Simons terms are present, namely the topological sector of ABJM theory and the family of bosonic latitude Wilson loops. In both cases, localization requires the use of non-standard supercharges and care must be taken to ensure off-shell closure of the SUSY algebra. I will present an explicit procedure for doing this in the case of bosonic latitude WL's in ABJM theory, recovering the associated matrix model. I will then argue for a dual realization of this loop as a novel bound state of Wilson and vortex loops, defined using supersymmetric quantum mechanics. Finally, I will briefly touch on the possibility of constructing a topological sector inside the DCFT defined by the 1/2 BPS "fermionic" WL in ABJM theory.

**Yfei He ****- slides**

**S-matrix bootstrap in 3+1 dimensions: regularization and the dual problem. **The S-matrix bootstrap maps out the space of S-matrices allowed by analyticity, crossing and unitarity. For 2-to-2 scattering, such space is an infinite dimensional convex space whose boundary can be approached by maximizing a linear functional. In this talk I will describe S-matrix bootstrap in 3+1 dimensions with focus on the equivalent dual problem which provides strict upper bounds for the regularized primal problem. The dual problem has interesting practical and physical advantages over the primal problem, and its variables are the dual partial waves who are free from constraints yet directly related to the physical partial waves. The formulation is done in the context of scalar fields related to pion physics. This talk is based on https://arxiv.org/abs/2103.11484 with Martin Kruczenski.

**Dennis Le Plat ****- slides**

**Integrable bootstrap for AdS3/CFT2 correlation functions.** I will discuss the integrable bootstrap framework proposed in 2102.08365 for the computation of correlation functions for superstrings in AdS_3 x S^3 x T^4 backgrounds supported by an arbitrary mixture or Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz fluxes. After reviewing some results of integrability for AdS_3 x S^3 x T^4, I will explain how to work out the hexagon form factor for two-particle states, including its dressing factors which follow from those of the spectral problem, and how to use them to compute arbitrary correlations functions. I will present a check with some correlation functions of protected operators, and discuss future directions for this research.

**Fedor Levkovich-Maslyuk ****- slides**

**Matrix Models for Dually Weighted Graphs and 2d Quantum Gravity.** I will describe a modified Hermitian one-matrix model whose perturbative expansion counts dually weighted graphs (DWG) that carry couplings not only for n-valent vertices but also for n-valent faces of the graph. The new couplings offer a powerful way to control the shape of the graphs and the resulting 2d geometries in the continuum limit. I will review old results on DWG, including the computation of Schur characters for a large Young tableau and the algebraic curve for counting planar quadrangulations. Then I will present new results from my upcoming paper with V. Kazakov where we count the disc quadrangulations with large, macroscopic area and boundary.

This allows us to extract an interesting continuous limit of fluctuating 2d geometry, interpolating between the “almost” flat disc with a few dynamical conical defects and the disc partition function for pure 2d quantum gravity, generalizing old results for the spherical topology. I will also speculate on the perspectives of describing JT gravity and looking for a discretization of AdS via a DWG model.

**Sergei Lukyanov ****- slides**

**Generalized affine sl(2) Gaudin model.** The focus of the talk is a certain generalization of the sl(2) quantum affine Gaudin model, which fits into the framework of Yang-Baxter integrability. We’ll discuss how to construct the mutually commuting set of Hamiltonians and calculate their spectrum within the ODE/IQFT approach

**Thomas Mertens ****- slides**

**Structure of JT boundary correlation functions.** In this talk, I will describe a certain class of boundary correlation functions in Jackiw-Teitelboim (JT) gravity. The focus is on some of the structural aspects of these correlators. After giving an overview of how the exact calculations work, I will discuss a subset of these corresponding to "degenerate" operator insertions. Finally, I will embed these calculations in Liouville gravity and the minimal string, and use this perspective to shed light on some puzzles one faces when considering boundary correlators at higher order in the genus expansion.

**Chiara Paletta ****- slides**

**Integrable open quantum system.** In nature, the interaction of a system with the environment cannot beavoided. Under certain conditions, the density matrix evolves through the so-called Lindblad equation. By using the boost automorphism mechanism, I will show how to construct one-dimensional integrable Lindblad systems. In particular, I will show some of the models given in PRL 126.24 (2021): 240403. One of them is equivalent to the Hubbard model with imaginary coupling. Another one has very interesting physical features: the non-equilibrium steady state is a current carrying mixed state, it is an integrable example of the pumping effect. I will furthermore discuss the relation between the Lindblad operator and Markovian processes. Furthermore, I will discuss our method for models of spin s=1.

**Joao Penedones ****- slides**

**Where is String Theory?** I will review the (numerical) S-matrix Bootstrap approach to scattering amplitudes. In particular, I will explain how this approach can be used to bound the space of Wilson coefficients in Effective Field Theories (EFT). I will focus on the application to supergravity in 10 spacetime dimensions (https://arxiv.org/abs/2102.02847). Remarkably, strongly coupled string theory seems to saturate the bounds imposed by Lorentz invariance, unitarity and causality.

**Leonardo Santilli ****- slides**

**New deformations of 2d Yang-Mills theories.** I will discuss deformations of two-dimensional QFTs introduced in recent years, mainly focusing on Yang-Mills theories. The first part of the talk will consist of a review of the integrability-preserving perturbation by the operator TTbar. Then, I will describe in detail the TTbar-deformation of 2d Yang-Mills theories. Finally, I will present a new deformation of Yang-Mills in 2d, derived from dimensional reduction on a squashed three-sphere.

Based on joint works with Richard J. Szabo and Miguel Tierz.

**Fiona Seibold ****- slides**

**S matrices for quantum-deformed superstrings.** I will discuss the worldsheet scattering theory of certain integrable deformations of AdS superstrings with quantum group symmetries. I will start by explaining why different such deformations can be constructed, depending on the choice of Dynkin diagram of the undeformed symmetry algebra. We will then see that the different exact S matrices solve the quantum Yang-Baxter equation and are related to one another by a Drinfel'd twist. Their expansion match the tree-level S matrices from perturbative calculations. Based on joint work with Stijn van Tongeren and Yannik Zimmermann.

**Didina Serban ****- slides**

**The q-deformed Haldane-Shastry model.** The talk will present the solution of a quantum deformation, XXZ-like, of the isotropic long-range model named after Haldane and Shastry. While its algebraic structure, including the symmetry, was known for a long time, the explicit expression for the highest weight wave functions in terms of Macdonald polynomials was derived only recently by Lamers, Pasquier and Serban, arXiv:2004.13210. The central ingredient of the solution is the concept of double Hecke algebra and its relation to a more general model, the Macdonald-Ruijsenaars spin model. This type of models is a rare example of long-range spin chains whose integrable algebraic structure is explicitly known and as such they are important to study both from the mathematical and physical point of view.

**Anne Spiering ****- slides**

**Integrability and chaos in SYM theories from anomalous-dimension spectra.**