# Integrability in Gauge and String Theory 2018 IGST 2018

Europe/Copenhagen
Festauditoriet (Copenhagen University)

### Festauditoriet

#### Copenhagen University

Bülowsvej 17, 1870 Frederiksberg C
Description

IGST 2018

The IGST conference series aims at bringing together leading experts as well as early stage researchers working on integrable structures underlying gauge and string theory.  Tools of integrability continue to provide us with sophisticated means of acquiring crucial novel insight into a large class of models of interest for high energy physics as well as condensed matter physics and mathematics. IGST 2018 is dedicated to the presentation of the most recent developments along these lines with special emphasis on, but not limited to, holographic set-ups.

Topics to be covered include integrability in relation to correlation functions and Wilson loops, the conformal bootstrap program, scattering amplitudes, entanglement entropy, tensor models, defect CFT’s and much more.

Speakers include

• Fernando Alday
• Till Bargheer
• Benjamin Basso
• Niklas Beisert
• Jacob Bourjaily
• Simon Caron-Huot
• Lucia Cordova
• Kevin Costello
• Robert de Mello Koch
• Johanna Erdmenger
• Simone Giombi
• Nikolay Gromov
• Yunfeng Jiang
• Juan Maldacena
• Elli Pomoni
• Balazs Poszgay
• Leonardo Rastelli
• Volker Schomerus
• Amit Sever
• Alessandro Sfondrini
• Bogdan Stefanski
• Matthias Wilhelm
• Konstantin Zarembo

Registration has closed. The deadline for registration was August 1st.

Organizing committee

• Marco Bianchi
• Troels Harmark
• Charlotte Kristjansen
• Kasper Vardinghus
• Matthias Wilhelm

• Romuald Janik
• Didina Serban
• Matthias Staudacher
• Pedro Vieira

Venue

The Conference will be held at Auditorium A1-01.01 in the Faculty of Life Sciences of Copenhagen University, Bülowsvej 17, 1870 Frederiksberg C, see map.

This conference is funded by DFF-FNU through their Sapere Aude Top Researcher Program

Contact
Conference Secretary Pia Kohring: kohring@nbi.ku.dk

Conference Organizers: igst2018@nbi.ku.dk

Contact
• Monday, August 20
• 8:30 AM 9:20 AM
Registration
• 9:20 AM 9:30 AM
Opening
• 9:30 AM 10:15 AM
Conformal Fishnet Theory 45m

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."

• 10:15 AM 11:00 AM
Coffee break 45m
• 11:00 AM 11:45 AM
Continuum limit of fishnet graphs and AdS sigma model 45m

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.

Speaker: Benjamin Basso
• 11:45 AM 12:30 PM

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.

Speaker: Bogdan Stefanski
• 12:30 PM 2:30 PM
Lunch break 2h
• 2:30 PM 3:15 PM
Non-planar holographic correlators from the analytic bootstrap 45m
Speaker: Luis Fernando Alday
• 3:15 PM 4:00 PM
Unifying correlators in AdS5xS5 supergravity 45m

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.

Speaker: Simon Caron Huot
• 4:00 PM 4:45 PM
Coffee break 45m
• 4:45 PM 5:30 PM
Schroedinger's Equation for Conformal Symmetry 45m

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.

Speaker: Volker Schomerus
• 6:00 PM 8:00 PM
Reception and poster session 2h
• Tuesday, August 21
• 9:30 AM 10:15 AM
Quantum corrections to holographic Wilson loops 45m

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.

Speaker: Konstantin Zarembo
• 10:15 AM 11:00 AM
Coffee break 45m
• 11:00 AM 11:45 AM
The Chiral Algebra Program for Four-Dimensional SuperConformal Field Theories 45m

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.

Speaker: Leonardo Rastelli
• 11:45 AM 12:30 PM
Bootstrapping 4d N=2 conformal theories 45m

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.

• 12:30 PM 2:30 PM
Lunch break 2h
• 2:30 PM 3:15 PM
One-point functions in defect CFT, Integrable Matrix Product States, and boundary integrability 45m

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.

Speaker: Balázs Pozsgay
• 3:15 PM 4:00 PM
d-dimensional SYK, AdS loops, and 6j symbols 45m

TBA

• 4:00 PM 4:45 PM
Coffee break 45m
• 4:45 PM 5:30 PM
Rationalizing Loop Integration 45m

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.

Speaker: Jacob Bourjaily
• Wednesday, August 22
• 9:30 AM 10:15 AM
Traversable wormholes 45m

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

Speaker: Juan Maldacena
• 10:15 AM 11:00 AM
Coffee break 45m
• 11:00 AM 11:45 AM
Yangian Symmetry and Correlation Functions in Planar N = 4 SYM 45m
Speaker: Niklas Beisert
• 11:45 AM 12:30 PM
Topological holography and the chiral algebra of N=4 gauge theory 45m

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.

Speaker: Kevin Costello
• 12:30 PM 6:00 PM
Free afternoon 5h 30m
• Thursday, August 23
• 9:30 AM 10:15 AM
Half-BPS Wilson line and defect 1d CFT 45m

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.

Speaker: Simone Giombi
• 10:15 AM 11:00 AM
Coffee break 45m
• 11:00 AM 11:45 AM
Integrability from Emergent Gauge Theory 45m

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.

Speaker: Robert de Mello Koch
• 11:45 AM 12:30 PM
Non-planar Scattering Amplitudes 45m

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.

Speaker: Amit Sever
• 12:30 PM 2:30 PM
Lunch break 2h
• 2:30 PM 3:15 PM
Counting instantons in N=1 theories of class Sk 45m

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.

Speaker: Elli Pomoni
• 3:15 PM 4:00 PM
The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve 45m

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.

Speaker: Matthias Wilhelm
• 4:00 PM 4:45 PM
Coffee break 45m
• 4:45 PM 5:30 PM
Quantum complexity in AdS/CFT and in quantum field theory 45m
Speaker: Johanna Erdmenger
• 7:00 PM 10:00 PM
Conference dinner 3h
• Friday, August 24
• 9:30 AM 10:15 AM
Quantum Spectral Curve and Structure Constants 45m
Speaker: Nikolay Gromov
• 10:15 AM 11:00 AM
Coffee break 45m
• 11:00 AM 11:45 AM
Handling Handles: Non-Planar AdS/CFT Integrability 45m

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.

Speaker: Till Bargheer
• 11:45 AM 12:30 PM
Planar and non-planar correlation functions in AdS/CFT 45m

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.

Speaker: Alessandro Sfondrini
• 12:30 PM 2:30 PM
Lunch break 2h
• 2:30 PM 3:15 PM
Adding flavour to the S-matrix bootstrap. 45m
Speaker: Lucía Gómez Córdova
• 3:15 PM 4:00 PM
Bethe ansatz and algebraic geometry 45m

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.

Speaker: Yunfeng Jiang
• 4:00 PM 4:30 PM
Closing 30m