Conformal Fishnet Theory

• Vladimir Kazakov

I review the last results for CFTs, proposed a couple of years ago by O.Gurdogan and myself, emerging as a double scaling limit of weakly coupled and strongly gamma-twisted N=4 SYM. This is a 3-coupling family of 4D non-unitary CFTs, integrable in planar limit. Its one parameter, bi-scalar reduction is often called "fishnet" CFT. It is generalized to any D dimensions. Among recent achievements, there is an exact computation of 4-point correlation functions of protected operators, providing a rich explicit OPE data, for "fishnet" CFTs, as well as for the full 3-parameter model. We also present the explicit computation of 2D analogue of Basso-Dixon fishnet 4-point function, directly from SL(2,C) spin chain formalism."

Continuum limit of fishnet graphs and AdS sigma model

• Benjamin Basso

I will discuss the thermodynamical limit of planar diagrams in the 4d fishnet theory, an integrable matrix scalar theory which stands as a close relative of the N=4 Super-Yang-Mills theory. Using integrable techniques developed for studying the scaling dimensions of single trace operators in N=4 SYM, I will argue that the continuum limit of the fishnet diagrams is governed by the 2d AdS5 non-linear sigma model.

AdS3/CFT2: Moduli and wrapping

• Bogdan Stefanski

I discuss two new findings in integrable AdS3/CFT2: the effect of turning on moduli, and incorporating massless wrapping corrections. The first result can be used to show that the AdS3 theory supported by pure NSNS flux is integrable. The second provides an intriguing link to an integrable description of two-dimensional CFTs first proposed by Al. B. Zamolodchikov, which arise in the present context as a low-energy limit of the integrable AdS3 theory.

Non-planar holographic correlators from the analytic bootstrap

• Luis Fernando Alday

Unifying correlators in AdS5xS5 supergravity

• Simon Caron Huot

We study correlation functions half-BPS operators in N=4 super Yang-Mills at strong coupling, dual to tree-level supergravity on AdS5xS5. We use techniques from the CFT toolkit: an inversion formula which expresses OPE data at this order as integrals over a finite sum of protected conformal blocks. The results for different spherical harmonics confirm recent conjectures, and reveal a striking simplicity: we show that the correlators fit together into a single ten-dimensional object, which enjoys a ``hidden’’ conformal invariance.

Schroedinger's Equation for Conformal Symmetry

• Volker Schomerus

Conformal partial wave expansions are an indispensable tool to separate the dynamical content of any conformal field theory from its kinematical skeleton. They can be used to analyze correlation functions of local and non-local fields, such as line- or surface operators, defects or interfaces. I will explain and exploit a remarkable relation with integrable multi-particle Schroedinger problems of Calogero-Sutherland type to develop a systematic theory of conformal partial waves for correlations of both local and non-local operators.

Quantum corrections to holographic Wilson loops

• Konstantin Zarembo

Area law for Wilson loops is one of the basic predictions of the AdS/CFT duality, valid at infinitely strong coupling. Going beyond the strict strong-coupling limit proved surprisingly difficult in this context, and quantum corrections had not been computed even for the simplest contours, such as the circular loop, until recently. I will describe the use of instanton calculus for Wilson loops in N=4 and N=2* SYM theories with the aim to compare the results with the exact predictions of localization.

The Chiral Algebra Program for Four-Dimensional SuperConformal Field Theories

• Leonardo Rastelli

Any ${\cal N}=2$ $4d$ superconformal field theory (SCFT) contains a subsector isomorphic to a $2d$ chiral algebra, or vertex operator algebra (VOA). The VOA computes a rich class of observables of the SCFT. In the opposite direction, four-dimensional physics expectations lead to interesting mathematical conjectures for VOAs. Most ambitiously, one hopes to use this $4d/2d$ correspondence as on organizing principle for the whole landscape of ${\cal N}=2$ SCFTs. In this talk, I will review the basics of the correspondence and describe some recent progress in characterizing the class of VOAs that descend from $4d$ SCFTs. The new insight is the VOA is intimately related to the low energy effective field theory on the Higgs branch of the $4d$ theory.

Bootstrapping 4d N=2 conformal theories

• Madalena Lemos

We review the conformal bootstrap approach to 4d N=2 superconformal field theories (SCFTs), and how it constrains the space of allowed theories. From the landscape of N=2 SCFTs we focus on the "simplest" interacting theory, an Argyres-Douglas theory, and approach it both with numerical bootstrap techniques and with the Lorentzian inversion formula. We conclude with an outlook for the prospects of approaching other Argyres-Douglas theories.

One-point functions in defect CFT, Integrable Matrix Product States, and boundary integrability

• Balázs Pozsgay

In a CFT with a defect the scaling operators can have non vanishing mean values. At one loop order in planar N=4 SYM the normalization constants of these one-point functions are given by the overlaps between the corresponding Bethe states and a particular Matrix Product State (MPS). These MPS are not eigenstates of the spin chain, but they display very special features: the overlaps are non-zero only for parity symmetric Bethe root configurations, and can be expressed in a factorized form. In this talk we focus on the algebraic properties of these MPS: we explain their relation to boundary integrability and the twisted Yangian, and show how they can be obtained from the twisted Boundary Yang-Baxter relation.

d-dimensional SYK, AdS loops, and 6j symbols

• Vladimir Rosenhaus

TBA

Rationalizing Loop Integration

• Jacob Bourjaily

I describe recent advances in our understanding of the functions that result from loop integration and the technology that exists to obtain these from local Feynman integrands.

Traversable wormholes

• Juan Maldacena

We discuss how to construction traversable wormholes in two and four dimensions. We will also discuss the same phenomenon in holographic theories.

Yangian Symmetry and Correlation Functions in Planar N = 4 SYM

• Niklas Beisert

Topological holography and the chiral algebra of N=4 gauge theory

• Kevin Costello

I'll describe a project joint with Davide Gaiotto to recover the chiral algebra for N=4 gauge theory, at large N, using holography in the topological string.

Half-BPS Wilson line and defect 1d CFT

• Simone Giombi

The half-BPS Wilson line in N=4 SYM preserves a 1d superconformal symmetry and can be viewed as a conformal defect of the 4d gauge theory. I will review some recent results for the "defect CFT1" defined by the correlation functions of operators inserted on the line, and its holographic duality to the string sigma model expanded around the AdS2 minimal surface. In particular, I will explain how to use supersymmetric localization to derive exact results for the correlators of a class of protected defect primaries of arbitrary length (reproducing, as a special case, known integrability results for the "generalized Bremsstrahlung function"). At strong coupling, the localization results are shown to precisely match the holographic calculation using the dual AdS2 worldsheet description.

Integrability from Emergent Gauge Theory

• Robert de Mello Koch

We study excitations of LLM geometries, formed by backreaction of a condensate of giant gravitons. Excitations of the condensed branes are open strings, which give rise to an emergent Yang-Mills theory at low energy. The dynamics of the planar limit of these emergent gauge theories match the planar N=4 super Yang-Mills. Three observations support this conclusion: (i) there is an isomorphism between operators of planar N=4 super Yang-Mills and the planar emergent gauge theory, (ii) the OPE coefficients of the planar emergent gauge theory vanish and (iii) the planar spectrum of anomalous dimensions of the emergent gauge theory is that of planar N=4 super Yang-Mills.

Non-planar Scattering Amplitudes

• Amit Sever

At higher orders in the 1/N expansion, scattering amplitudes receives contributions from diagrams of higher genus. We view these higher genus contributions as gluing of planar objects in momentum space. This is done by identifying the spacetime momentum that flows around the cycles of the 't Hooft surface. We focus on the first non-planar correction to gluon scattering amplitudes in N=4 SYM theory. The correction takes the form of a double trace partial amplitude and the corresponding 't Hooft surface has the topology of a cylinder. It is suppressed by one power of 1/N with respect to the leading single trace contribution. We extend the duality between planar scattering amplitudes and null polygonal Wilson loops to the double trace amplitude. The new duality relates the amplitude at any fixed momentum flow around the cylinder to the correlation function of two infinite null polygonal Wilson lines that are subject to a quantum periodicity constraint. We test the duality perturbatively at one-loop order and demonstrate it for the dual string in AdS. The duality allows us to extend the notion of the loop integrand beyond the planar limit and to determine it using recursion relations. It also allows us to apply the integrability-based pentagon operator product expansion approach to the first non-planar order.

Counting instantons in N=1 theories of class Sk

• Elli Pomoni

In this talk we will explain how to obtain the instanton partition functions of a large class of N=1 superconformal theories (SCFTs), called Sk. We will begin by introducing this class of N=1 SCFTs, which is obtained from Gaiotto’s class S of N=2 SCFTs via orbifolding. We can study the Coulomb branch of these theories by constructing and analyzing their spectral curves. Employing our experience with the AGT correspondence we will search for a 2D/4D relation for the N=1 SCFTs in class Sk. From the curves we can identify the 2D CFT symmetry algebra and its representations, namely the conformal blocks of the Virasoro/W-algebra, that underlie the 2D theory and reproduce the spectral curves of the N = 1 SCFTs. These conformal blocks give a prediction for the instanton partition functions of the 4D N = 1 SCFTs of class Sk. Finally, we will present a completely independent, elliptic genus calculation, counting open string states on Dp/D(p-4) brane systems in type IIB string theory, which exactly reproduces our previous result for the instanton partition functions.

The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve

• Matthias Wilhelm

We establish a framework for calculating the Hagedorn temperature of AdS$_5$/CFT$_4$ via integrability. Concretely, we derive Quantum Spectral Curve equations that yield the Hagedorn temperature of planar N=4 super Yang-Mills theory at any value of the 't Hooft coupling. We solve these equation perturbatively at weak coupling and numerically at finite coupling. Finally, we comment on extending these result to integrable deformations of N=4 SYM theory and on the inclusion of chemical potentials.

Quantum complexity in AdS/CFT and in quantum field theory

• Johanna Erdmenger

Quantum Spectral Curve and Structure Constants

• Nikolay Gromov

Handling Handles: Non-Planar AdS/CFT Integrability

• Till Bargheer

I will explain how to compute non-planar correlation functions in AdS/CFT at large N by integrability methods. The computation is based on a tessellation of the worldsheet into integrable hexagon patches, and it naturally includes a discretization of the string theory moduli space. The weak-coupling expansion is extremely efficient in the large-charge limit. Finite charges require a careful treatment of boundary effects.

Planar and non-planar correlation functions in AdS/CFT

• Alessandro Sfondrini

I will describe how to employ hexagonal tessellations to compute correlation functions, including 1/Nc non-planar corrections, in N=4 SYM and in the dual AdS5xS5 superstring. I will highlight the outstanding challenges inherent in the hexagon formalism, focusing on the difficulties in accounting for all "wrapping" finite-size corrections. I will then introduce a novel integrable model, the AdS3xS3xT4 superstring with no Ramond-Ramond flux; here the S-matrix is entirely given by a CDD factor and finite-size corrections to the spectrum vanish exactly, making this an extremely promising playground for the hexagon-tessellation program.

Adding flavour to the S-matrix bootstrap.

• Lucía Gómez Córdova

Bethe ansatz and algebraic geometry

• Yunfeng Jiang

In this talk, I will discuss how to apply methods of modern computational algebraic geometry to Bethe ansatz. I will show that algebraic geometry provides natural mathematical languages and powerful tools to understand the structure of solutions of Bethe ansatz equations (BAE). In particular, I will present new methods to count the number of physical solutions with fixed quantum numbers based on Gröbner basis and quotient ring. This method can be applied to study the completeness of Bethe ansatz. I will then discuss an efficient analytical method to compute the sum of on-shell physical quantities over all physical solutions without explicitly solving BAE. We apply this method to compute and study torus partition functions of the 6-vertex model at finite size. Finally, we find new internal structure of solution space of BAE and give the physical interpretations.