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### Timetable

Monday Tuesday Wednesday Thursday Friday
8:45-9:30 Registration
9:30-10:20 Tateo Vieira Okounkov Nekrasov Maldacena
10:20-10:50 Coffee break
10:50-11:40 Caetano Sobko Chicherin Marboe Bissi
11:40-12:30 Levkovich-Maslyuk Mitev Tourkine Kozlowski Zhiboedov
Lunch Whispers of String Theory
14:30-15:20 Loebbert Borsato Komatsu Tseytlin
15:20-16:10 Harmark Sfondrini Korchemsky Kristjansen
16:10-16:40 Coffee break Free Afternoon Coffee break
16:40-17:30 Bazhanov Tonni
Cocktail-Poster 18:30   Dinner 20:00

### Monday

 Roberto Tateo CDD ambiguity and irrelevant deformations of 2D QFT slides The study of 2D Quantum Field Theories perturbed by irrelevant operators is still a largely unexplored research topic. These perturbations may lead to singular RG flows where the UV fixed point is not well-defined. An important arena where such flows appear prominently is the study of effective string theories, such as the ones used to describe confining flux tubes in non-Abelian gauge models. In this talk will discuss various aspects concerning a special kind of integrable irrelevant perturbation corresponding to the composite operator $T \bar{T}$ and how it affects the energy levels of a generic 2D Quantum Field Theory, through a surprising relation with the inviscid Burgers equation. João Caetano Correlation Functions in Strongly Twisted  N=4 SYM slides Fedor Levkovich-Maslyuk Dipole CFTs, Bethe states and separation of variables slides I will discuss the dipole deformation of the N = 4 super Yang-Mills theory, which is an example of a potentially solvable nonrelativistic CFT. Its holographic dual is the Schrodinger space-time arising in many contexts in string theory. The deformation leads to a Drinfeld-Reshetikhin twist in the integrable structure and renders the conventional Bethe ansatz inapplicable from the very beginning. Instead I will present the Baxter equation capturing the 1-loop spectrum in the sl(2) sector and closely linked with separation of variables (SoV). I will show that the spectrum of long operators matches string theory predictions, providing a quantitative test of the Schrodinger holography. In the second part of the talk I will present an explicit realization of the SoV for SU(N) spin chains, leading to a new construction of their eigenstates. The states are built by repeatedly acting on the vacuum with a single operator Bgood evaluated at the Bethe roots. This provides a compact alternative to the usual nested Bethe ansatz. Florian Loebbert Master Symmetry and Wilson Loops in AdS/CFT slides We discuss a nonlocal master symmetry of symmetric space models that generates the spectral parameter and acts as a level-raising operator on the model’s Yangian charges. We apply this symmetry to smooth Wilson loops in strongly coupled AdS/CFT and make connection to the recently observed one-parameter deformations of minimal surface solutions. Troels Harmark Hagedorn temperature of AdS/CFT via integrability slides In this talk I review recent work with Matthias Wilhelm that establishes a framework for calculating the Hagedorn temperature of AdS5/CFT4 via integrability. After introducing the subject of the Hagedorn temperature in the AdS/CFT correspondence, I explain how the Hagedorn temperature is linked to the continuum limit of the free energy of the spin chain associated with the correspondence. This is computed in the direct theory, rather than in the so-called mirror theory that one uses for solving the spectral problem. I review the TBA equations that lead to the computation of the free energy. Finally, I explain briefly how we solved the TBA equations perturbatively, up to second order in the ’t Hooft coupling, deriving the previously unknown two-loop Hagedorn temperature.
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### Tuesday

 Pedro Vieira S-matrix Bootstrap. Integrable Theories and Non-Integrable Theories slides Evgeny Sobko Conformal blocks, harmonic analysis and Calogero-Sutherland models slides I will present a universal approach to spinning conformal blocks through the harmonic analysis of certain bundles over double coset of the conformal group. Surprisingly the resulting Casimir equations are given by a matrix version of the Calogero-Sutherland Hamiltonian. With minor modification, the same method can be applied to a case of boundary CFT. At the end of my talk, I will briefly discuss how to diagonalize this new family of Hamiltonians. Vladimir Mitev 2D CFTs for a class of 4D N=1 theories slides In this talk I will present our program for the search for the 2D CFT description of a large class of 4D  gauge theories with superconformal N=1 symmetry. I will show how to 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 Seiberg-Witten curves of the N=1 gauge theories. One finds that the blocks corresponding to the gauge theories under investigation involve fields in certain non-unitary representations of the Virasoro/W-algebra algebra. Furthermore, these conformal blocks give a prediction for the instanton partition functions of the 4D theories. Riccardo Borsato q-Poincaré supersymmetry in AdS5/CFT4 slides I will discuss the paper arXiv:1706.10265, where we show that the exact S-matrix governing the planar spectral problem for strings on AdS5 x S5 and N=4 super Yang-Mills is invariant under a novel "boost" symmetry, which acts as a differentiation with respect to the particle momentum. This generator leads us also to reinterpret the usual centrally extended psu(2|2) symmetry, and to conclude that the S-matrix is invariant under a q-Poincaré supersymmetry algebra, where the deformation parameter is related to the 't Hooft coupling. We determine the two-particle action (coproduct) that turns out to be non-local, and study the property of the new symmetry under crossing transformations. We look at both the strong-coupling (large tension in the string theory) and weak-coupling (spin-chain description of the gauge theory) limits; in the former regime we calculate the cobracket utilising the universal classical r-matrix of Beisert and Spill. In the eventuality that the boost has higher partners, we also construct a quantum affine version of 2D Poincaré symmetry, by contraction of the quantum affine version of su(2) in Drinfeld's second realisation. Alessandro Sfondrini Latest news from AdS3/CFT2 slides I will report on the latest developments in the study of the AdS3/CFT2 spectral problem by integrability. I will discuss the AdS3xS3xT4 and AdS3xS3xS3xS1 backgrounds supported by a mixture of Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three-form fluxes, and derive their BPS spectrum, commenting on how this squares with our understanding of their holographic duals. Vladimir Bazhanov Towards Canonical Quantization of Non-Linear Sigma-Models slides In this talk we revisit the problem of canonical quantization of two-dimensional non-linear sigma models (NLSM) in two dimensions. We unravel the integrability structure of the O(3) NLSM and its one-parameter deformation --- the sausage model. Our consideration is based on the continuous version of the Quantum Inverse Scattering Method enhanced by a powerful ODE/IQFT correspondence, which connects stationary states of Integrable QFT models with special solutions of classical integrable equations. Among the obtained results is a system of non-linear integral equations for computation of vacuum eigenvalues of the continuous analogs of quantum transfer-matrices for the O(3)/sausage NLSM. The talk is based on the recent article arXiv:1706.09941 (joint with Gleb Kotousov and Sergei Lukyanov).
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### Wednesday

 Andrei Okounkov Gauge theories and Bethe eigenfunctions slides The talk will be based on a joint paper https://arxiv.org/abs/1704.08746 with Mina Aganagic. In this paper, we essentially complete the program of Nekrasov and Shatashvili who explained the meaning of Bethe roots, Bethe equations, etc. of quantum integrable systems via their correspondence with supersymmetric gauge theories. We explain the meaning of off-shell Bethe eigenfunctions (which also give solutions of the quantum Knizhnik-Zamolodchikov equations and related difference equations). Our formulas may be seen from a geometric, representation–theoretic, combinatorial, and other angles. Dmitry Chicherin Yangian Symmetry of Fishnet Graphs slides We consider an all-loop conformal Yangian symmetry of fishnet graphs. These multipoint Feynman graphs correspond to several interesting observables in the integrable massless bi-scalar field theory in four dimensions. The on-shell graphs constitute the full set of planar amplitudes, and the off-shell graphs describe single-trace correlators. The Yangian is realized as the monodomry matrix acting on the boundary of fishnet graphs that provides a number of differential equations for them. We also discuss generalizations for graphs with fermions and for scalar graphs in three and six dimensions. Piotr Tourkine Towards the S-matrix of massless QFTs on the Riemann sphere slides Scattering amplitudes are crucial in high energy physics. They bridge the gap between theory and experiment, and major progress over the last 25 years have lead us to discover an unexpected simplicity underlying the theories that describe nature (gauge, gravity). In this talk I aim to introduce an elegant formalism that takes a radically new look to the computation of S-matrix elements, based on the Cachazo-He-Yuan formulae and the Mason-Skinner or ambitwistor string. I will start by introducing the formalism and describing recent developments. I’ll present some results in collaboration with two distinct groups (*). The first part will concern the extension of this formalism to loops. In the second I’ll argue that the relation of this new formalism to standard string theory may use a special kind of string theory called “null strings”, whose quantization give rise to ambitwistor strings. This program gives the hope to be able to develop a complete reformulation of the loop expansion in QFTs. (*): (Geyer-Mason-Monteiro; Casali-Herfray)
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### Thursday

 Nikita Nekrasov Tying instantons to anti-instantons using gauge theory and integrability slides Christian Marboe Old roots in new equations slides I will revisit the spectrum of single-trace operators in N=4 SYM, and describe how to classify the irreducible representations of the superconformal symmetry that they form, in terms of a non-compact generalisation of Young diagrams. These multiplets are in one-to-one correspondence to “rational” solutions to a Q-system. Traditionally, this Q-system is defined by the algebra in question, but I will argue that it lives a more natural, algebra-independent life on the corresponding Young diagram. Using this intuition, I will present a simple algorithm to solve such systems, providing a cleaner and more powerful alternative to Bethe equations. These solutions form the starting point for perturbative calculations of anomalous dimensions via the Quantum Spectral Curve. I will sketch a conceptually very simple method to do such calculations for general states, discuss patterns in the results, and speculate about how to get more info out of the QSC. Karol Kozlowski On singularities of dynamic response functions in the massless regime of the XXZ chain slides I will explain how, starting from the large-volume behaviour of the form factors of local operators, one can construct  the thermodynamic limit of the massless form factor expansion of dynamical two-point functions in the XXZ chain.  The massless form factor expansion provides one with an efficient tool allowing one to fully describe the singular behaviour of the  dynamic response functions - i.e. the space and time Fourier transforms of two-point functions.  The characterisation of the singular structure of the response function obtained in this work builds on a first principle based analysis carried directly at the microscopic level.  On top of being free from any hypothetical correspondence with a field theory, the analysis unravels a new class of edge exponents stemming from collective  excitations, which was not accounted for by the existing heuristic approaches.  Finally, the analysis provides a  very simple picture allowing one to reduce the manifestation of universal features characteristic of the Luttinger Liquid universality class to the presence of certain singularities in the form factors of local operators and to consequences of a classical asymptotic analysis of multiple integrals. Shota Komatsu Hexagonalization of Correlation Functions in N=4 SYM slides I will explain a nonperturbative framework to study general correlation functions of single-trace operators in N=4 supersymmetric Yang-Mills theory at large N. The basic strategy is to decompose them into fundamental building blocks called the hexagon form factors, which were introduced earlier to study structure constants using integrability. The decomposition is akin to a triangulation of a Riemann surface, and we thus call it hexagonalization. I then propose a set of rules to glue the hexagons together based on symmetry, which naturally incorporate the dependence on the conformal and the R-symmetry cross ratios. I will show how it works in practice using explicit examples at weak coupling. I will also comment on other related developments, including some relation to pentagon OPE and the generalization to open strings. This talk will be based mostly on the work done with Thiago Fleury. Gregory Korchemsky Catching integrability with fishnets and instantons slides Erik Tonni Corner contributions to holographic entanglement entropy in AdS4/BCFT3 slides In the context of the AdS4/BCFT3 correspondence, where also the gravitational spacetime is bounded by a hypersurface which encodes the boundary conditions characterising the dual BCFT3, we study the holographic entanglement entropy of spatial regions with corners, whose vertices are located on the boundary of the BCFT3. The case where the boundary of the BCFT3 is a flat hyperplane is considered. Analytic expressions for the simplest corner functions are presented. A numerical analysis is performed by computing the area of the minimal area surfaces corresponding to finite domains.
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### Friday

 Juan Maldacena The SYK model and nearly-AdS2 gravity slides Agnese Bissi Loop corrections to supergravity slides In this talk I will discuss how to extract 1/N^4 corrections to anomalous dimensions of intermediate operators from the four point correlator of the stress-energy tensor multiplet in N=4SYM, at large ’t Hooft coupling. This corresponds to loop corrections to the supergravity result. Alexander Zhiboedov Bootstrap for Large N Confining Gauge Theories slides Arkady Tseytlin Fluctuations of BPS Wilson loop and AdS2/CFT1 slides We discuss correlation functions of local operator insertions on the 1/2-BPS Wilson line in N = 4 super Yang-Mills theory. These correlation functions define a defect CFT1 living on the line. At strong coupling, a set of elementary operator insertions with protected scaling dimensions correspond to fluctuations of the dual fundamental string in AdS5 × S5 ending on the line at the boundary and can be thought of as light fields propagating on the AdS2 worldsheet. We compute the tree-level AdS2 Witten diagrams describing the strong coupling limit of the four- point functions of the dual operator insertions. In the case of the circular Wilson loop, we match our results for the 4-point functions of a special type of scalar insertions to the prediction of localization to 2d Yang-Mills theory. Charlotte Kristjansen One- and two-point functions of AdS/dCFT slides
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