Niklas Beisert “Smooth Wilson Loops in N = 4 Superspace and Yangian Symmetry” slidesvideo We consider smooth Maldacena-Wilson loops in N=4 super Yang-Mills theory. As supposedly finite observables with large-N disk topology, they are ideally suited to study Yangian symmetry. We construct these objects in full N=4 superspace and derive the action of the conformal and Yangian algebra on them in detail. This allows us to show Yangian invariance of the planar one-loop expectation value paying particular attention to boundary contributions and renormalisation. It also helps towards defining a more concrete notion of integrability in this model. Joao Caetano OPE for all Helicity Amplitudes slidesvideo We extend the Operator Product Expansion (OPE) for scattering amplitudes in planar N=4 SYM to account for all possible helicities of the external states. This is done by constructing a simple map between helicity configurations and so-called charged pentagon transitions. These OPE building blocks are generalizations of the bosonic pentagons entering MHV amplitudes and they can be bootstrapped at finite coupling from the integrable dynamics of the color flux tube. A byproduct of our map is a simple realization of parity in the super Wilson loop picture. Sergei Dubovsky Approximate Integrability on the Worldsheet of the QCD String slidesvideo I will review recent progress in the study of the QCD strings (flux tubes) based on calculating the flux tube spectra from the worldsheet S-matrix through Thermodynamic Bethe Ansatz. Simone Giombi Generalized F-theorem and the epsilon-expansion slidesvideo I will discuss the dimensional continuation of the sphere free energy in conformal field theory. In particular, I will provide evidence for a "generalized F-theorem" smoothly interpolating between a-theorems in even dimensions and F-theorems in odd dimensions. As an application, I will explain how to use the Wilson-Fisher epsilon expansion to estimate the value of F for the d=3 Ising CFT and related models with O(N) symmetry. Jaume Gomis Loop Operators and Mirror Symmetry slidesvideo Wilson loops in gauge theories pose a fundamental challenge for dualities. Wilson loops are labeled by a representation of the gauge group and should map under duality to loop operators labeled by the same data, yet generically, dual theories have completely different gauge groups. In this paper we resolve this conundrum for three dimensional mirror symmetry. We show that Wilson loops are exchanged under mirror symmetry with Vortex loop operators, whose microscopic definition in terms of a supersymmetric quantum mechanics coupled to the theory encode in a non-trivial way a representation of the original gauge group, despite that the gauge groups of mirror theories can be radically different. Our predictions for the mirror map, which we derive guided by branes in string theory, are confirmed by the computation of the exact expectation value of Wilson and Vortex loop operators on the three-sphere. Ben Hoare On eta- and lambda-deformations of AdSn x Sn supercosets slidesvideo In this talk we will discuss two integrable deformations of supercoset sigma models associated to strings moving in AdS_n x S^n backgrounds. These are the so-called eta- and lambda-deformations and both are conjectured to be related to quantum group deformations of the underlying symmetry algebra. The former is based on the Yang-Baxter sigma model, named for its dependence on a solution of the modified classical Yang-Baxter equation, and is a deformation of the standard superstring action on AdS_n x S^n. The latter is based on a deformed gauged WZW model and interpolates to the non-abelian T-dual of the AdS_n x S^n superstring. After introducing the two deformations and highlighting some key features, we will explore the relation between the two models, showing that the eta-deformed model may be obtained from the lambda-deformed one by a special scaling limit and analytic continuation. The relation between the couplings and deformation parameters is consistent with the interpretation of the first model as a real quantum deformation and the second as a root of unity quantum deformation. Depending on time we will then briefly outline the effect of this limit on the supergravity background associated to the lambda-deformed model in the AdS_2 x S^2 case. Tim Hollowood The q Deformed Superstring slidesvideo We describe various features of the one of the recently discovered integrable deformations of the superstring in AdS_5 x S^5 known as the q deformation. Romuald Janik Towards the AdS5xS5 string field theory vertex slidesvideo In this talk I will describe progress on using integrability to construct the light cone string field theory vertex in case the worldsheet theory is integrable and discuss some specific aspects in the case of AdS5xS5. Fedor Levkovich-Maslyuk Numerical Solution of the Spectral Problem and NNLO BFKL in N=4 SYM slidesvideo I will present an efficient numerical algorithm for computing the spectrum of anomalous dimensions of the planar N=4 Super-Yang--Mills at finite coupling. The method is based on the Quantum Spectral Curve formalism. In particular, it is possible to compute the BFKL pomeron intercept in a wide range of the ''t Hooft coupling constant with ~20 significant digits precision, and to explore a rich branch cut structure for complexified spin S in the sl(2) sector. I will also present an analytic result for the NNLO BFKL eigenvalue, obtained from an iterative solution of the QSC and confirmed by many checks. Tomasz Lukowski Large spin systematics in CFT slidesvideo In this talk I will discuss how using conformal field theory arguments to derive an infinite number of constraints on the large spin expansion of the anomalous dimensions and structure constants of higher-spin operators. The results are valid for both, perturbative CFT to all orders in the perturbation parameter, as well as non-perturbatively. For the case of conformal gauge theories this provides a proof of the reciprocity principle to all orders in perturbation theory and provides a new ,,reciprocity'''' principle for structure constants. Sergei Lukyanov Winding vacuum energies in a deformed O(4) sigma model slidesvideo We consider the problem of calculating the Casimir energies in the winding sectors of Fateev''s SS-model, which is an integrable two-parameter deformation of the O(4) non-linear sigma model in two dimensions. This problem lies beyond the scope of all traditional methods of integrable quantum field theory including the thermodynamic Bethe ansatz and non-linear integral equations. Here we propose a solution based on a remarkable correspondence between classical and quantum integrable systems and express the winding energies in terms of certain solutions of the classical sinh-Gordon equation. Lionel Mason Ambitwistor Strings and amplitudes slidesvideo Recently remarkable formulae for tree-level scattering amplitudes have been found for gauge and gravity theories based on the scattering equations''. I will explain how these arise from string theories in ambitwistor space and some developments of the ideas to understand other theories, soft theorems and extensions to loop integrands. Joseph Minahan Supersymmetric gauge theories in higher dimensions slidesvideo I discuss how to put maximally supersymmetric gauge theories on spheres. In particular I consider the six and seven dimensional cases and compute their perturbative partition functions. Sanefumi Moriyama Superconformal Chern-Simons Theories from Fermi Gas Approach slidesvideo ABJM theory, describing M2-branes on a simple orbifold, enjoys many interesting properties: the free energy obeys the 3/2 power law; the perturbative corrections are summed up to Airy function; the non-perturbative corrections are described by refined topological string theory. There is an assembly of superconformal Chern-Simons theories describing M2-branes on more general backgrounds which share the properties. These properties often stem from a description of the theory with a Fermi gas system. I will explain that the relation to the Fermi gas is broader than originally expected. Namely, besides quiver gauge theories of affine A type, the Fermi gas description works also for quivers of affine D type and quivers with different ranks (ABJ). Vasilis Niarchos Exact correlation functions in 4d N=2 superconformal field theories slidesvideo I will discuss recent exact results for extremal correlation functions in the N=2 chiral ring of four-dimensional N=2 superconformal field theories with non-trivial superconformal manifolds. Special emphasis will be given to the case of SU(N) superconformal QCD theories where a new solution of the tt* equations will be proposed. Elli Pomoni TN partition functions and Toda 3-point functions slidesvideo Even though the TN theories have no Lagrangian description, we are able to derive their partition functions using 5-brane junctions and topological strings. Through the AGTW correspondence, we relate them to the 3-point functions of 2D Toda CFT with all three primaries arbitrary. Our proposed formula, has the correct symmetry properties, zeros and for N = 2 it gives the DOZZ answer for Liouville CFT. Finally, when we choose one of the primaries to have a null-vector descendant at level one we obtain from it the well-known formula by Fateev and Litvinov, thus presenting a highly non-trivial check of our proposal. Radu Roiban On the eta-deformed background and its scattering states slidesvideo After a brief review of the supergravity solutions whose NSNS part is given by the eta-deformed AdS x S metric and B field, we discuss the calculation of higher-loop corrections to the scattering matrix of worldsheet excitations around the BMN vacuum state. The expected S matrix is reproduced provided that the naive asymptotic excitations are redefined in a nontrivial way, a feature that is absent if the deformation is removed. We also briefly discuss some probes of this space and, if time allows, other possible deformations. Fedor Smirnov Form factors for relativistic and lattice models slidesvideo In this talk I shall review the form factor bootstrap for relativistic models. The Local Commutativity Theorem will be discussed. Then I shall discuss the relation to the lattice models. Certain unsolved problems will be underlined. Bogdan Stefanski Integrability and the Conformal Field Theory of the Higgs branch slidesvideo I will show how integrability emerges in the Higgs branch CFT2 and how this integrable structures matches with the one found in the dual AdS3 theory. Jon Toledo Smooth Wilson loops in N=4 from integrability slidesvideo In this talk I will present integral equations for the area of minimal surfaces in AdS_3 ending on generic smooth boundary contours. I will sketch how the equations are derived from the continuum limit of the AMSV result for null polygonal boundary contours. I will also comment on the modification of the equations appropriate for a euclidean boundary and the connection with the theta-function construction of Ishizeki, Krucsenski and Ziamma. Gabriele Travaglini The dilatation operator of N=4 SYM, amplitudes and Yangian symmetry slidesvideo In this talk we discuss connections between scattering amplitudes and on-shell methods, and the dilatation operator of N=4 super Yang-Mills. We will first apply a method originally devised for computing scattering amplitudes known as MHV diagrams to the derivation of the one-loop dilatation operator in the SO(6) sector. We then show the same calculation in a fully on-shell way using generalised unitarity and extend it to the SU(2|3) sector. In the second part of the talk we show the Yangian symmetry of the tree-level S-matrix of N=4 super Yang-Mills implies the Yangian invariance, up to boundary terms, of the one-loop complete dilatation operator. Pedro Vieira \sqrt{C_{123}} video I will review our recent construction (with B. Basso and S. Komatsu) on the hexagon program for computing structure constants in N=4 SYM at any coupling. In this approach, the structure constant is broken down into more elemental building blocks - the hexagons - which we can tackle by means of an integrable bootstrap of sort. Time permitting, we will also comment on various non-trivial checks agains other approaches such as the conformal block expansion of four point correlation functions or tailoring inspired methods (at weak coupling) and string minimal areas (at strong coupling). Dmytro Volin Behind Quantum Spectral Curve slidesvideo I will review the recent progress in explicit solution of the quantum spectral curve for AdS5/CFT4 integrable system, show how one can deform it by introducing twists, and discuss how we should perceive the curve in a more general context of quantum integrable models. This discussion will include an example of a system different from AdS5/CFT4, namely the Hubbard model. Masahito Yamazaki Gauge/YBE Correspondence slidesvideo I will describe recent progress in uplifting Yang-Baxter Equations (with spectral parameters) into dualities (Yang-Baxter dualities) in supersymmetric gauge theories in various dimensions. Many solutions of Yang-Baxter equations could be systematically constructed by computing various supersymmetric partition functions. Konstantin Zarembo One-point functions video In the presence of heavy probes such as domain walls, Wilson or ''t Hooft loops, external metric etc, one-point functions of local operators becomes non-trivial. In the spin-chain language, they map to overlaps of Bethe states with some fixed state associated with the defect. I will describe how one-point function in the presence of a domain wall can be computed using integrability. In the su(2) sector the problem reduces to overlaps with the Matrix Product State and N?el-type states. Shota Komatsu The uses of SoV in 3pt functions at weak coupling slidesvideo We discuss the application of Sklyanin''s separation of variables (SoV) to the 3pt functions in the SU(2) sector of N=4 SYM at weak coupling. After reviewing the basics of SoV, we derive an explicit expression for the SoV basis with twisted boundary conditions and the overlap between the orginal SoV state and the SoV states for the subchains. We then derive an integral expression for 3pt functions by first mapping the problem to the paritition function of six-vertex model with a hexagonal boundary and applying the SoV to the `auxiliary space". Johannes Henn The 3-loop QCD cusp anomalous dimension slidesvideo The 3-loop QCD cusp anomalous dimension