## Speakers

The confirmed speakers are listed below, together with the tentative titles and abstracts of the talks.

 Zoltan Bajnok We analyze the spectrum of open strings stretched between a D-brane and an anti-D-brane in planar AdS/CFT using various tools. We focus on open strings ending on two giant gravitons with different orientation in AdS_5xS^5 and study the spectrum of string excitations using the following approaches: open spin-chain, boundary asymptotic Bethe ansatz and boundary thermodynamic Bethe ansatz (BTBA). We find agreement between a perturbative high order diagrammatic calculation in N=4 SYM and the leading finite size boundary Lüscher correction. We study the ground-state energy of the system at finite coupling by deriving and numerically solving a set of BTBA equations. While the numerics give reasonable results at small coupling, they break down at finite coupling when the total energy of the string gets close to zero, possibly indicating that the state turns tachyonic. "Brane--anti-brane system from an integrable point of view" Benjamin Basso In planar N=4 Super-Yang-Mills theory there is a map between gluons scattering amplitudes and null polygonal Wilson loops. This remarkable duality allows one to make an important step forward by Operator-Product-Expanding the scattering amplitudes. This action breaks down the four-dimensional amplitudes into a sequence of two-dimensional processes taking place on the flux tube sourced by the dual Wilson loops. In this talk I will explain how the integrable structures of the flux tube theory can be used for computing scattering amplitudes this way regardless of the value of the coupling. "Space-Time S-matrix and Flux-Tube S-matrix: Part II" Agnese Bissi In this talk I will discuss the three-point correlator of two protected scalar operators and one higher spin twist-two operator in N = 4 SYM, in the limit of large spin. This structure constant can be extracted from the OPE of the four-point correlator of protected scalar operators. Based on the OPE structure, symmetry arguments and intuition from the available perturbative results, it is possible to predict the structure constant at all loops in perturbation theory. This allows also to propose an expression for the all loops four-point correlator in a particular limit. "Higher-spin correlators" Luigi Cantini In 2001 Razumov and Stroganov conjectured that the (properly normalized) components of the ground state of the dense O(1) loop model on a semi-infinite cylinder enumerate fully-packed loop (FPL) configurations on the square, with alternating boundary conditions, refined according to the link pattern for the boundary points. The correspondence between these apparently unrelated subjects and their rich combinatorial content have arisen a lot of interest both in the physics and in the mathematics community. In this talk we present the subject with a focus on the implications of the integrable structure of the loop model on the Enumerative Combinatorics of FPL and other combinatorial objects such as Alternating Sign Matrices. "Razumov-Stroganov–type Correspondences: combinatorics and integrability" Rouven Frassek Inspired by Baxter’s perimeter Bethe ansatz we present a method to construct Yangian invariants. The condition for Yangian invariance is formulated as an eigenvalue problem of certain monodromies that can be solved using Bethe ansatz techniques. The rather general principle is being worked out for rational inhomogeneous spin chains with finite-dimensional representations of gl(n) in the quantum space. Using the algebraic Bethe ansatz we derive Bethe ansatz equations for Yangian invariants and study the corresponding on-shell Bethe vectors. Furthermore, we show how they can be reformulated in terms of contour integrals. This aspect is reminiscent of an on-shell formulation of scattering amplitudes in N=4 super Yang-Mills theory. "Bethe Ansatz for Yangian Invariants: Towards Scattering Amplitudes" Matthias Gaberdiel The conjectured relation between higher spin theories on AdS spaces and weakly coupled conformal field theories is reviewed. I shall then explain the evidence in favour of a concrete duality of this kind, relating a specific higher spin theory on AdS3 to a family of 2d minimal model CFTs. Finally, I shall describe recent progress towards relating these higher spin theories to string theory. "Large N=4 Minimal Model Holography" Nikolay Gromov We give several examples of solutions of the recently proposed by NG, Kazakov, Leurent and Volin equations describing simple and efficient underlying integrability structure of AdS5/CFT4. "Quantum spectral curve at work" Romuald Janik The use of twist-two operators in the BFKL regime typically involves an analytical continuation in the spin from the physical integer values. This procedure is performed once an analytical exact answer for the anomalous dimensions in terms of harmonic sums has been found. In this talk I identify the analytic conditions for the solution of Baxter equation which gives the above result directly for any complex spin up to two loops. I also comment on strong coupling classical string solutions relevant for the BFKL regime. "BFKL regime, twist-two operators and classical solutions" Gregory Korchemsky We discuss the relation between dual superconformal symmetry in planar N = 4 SYM and integrability of dilatation operator in the same theory. We demonstrate that this symmetry is powerful enough to ﬁx the eigenspectrum of the dilatation operator in the SL(2) sector and supersymmetric extension to the lowest order in the coupling. We use the relation between the one-loop dilatation operator and Heisenberg spin chain to show that, to lowest order in the coupling, the dual symmetry is generated by the Baxter Q−operator in the limit of large spectral parameter. "Dual conformal symmetry and integrability" Ivan Kostov We present some exact results about the tree-level 3-point function of local single-trace operators in the scalar sector of planar N = 4 supersymmetric Yang-Mills. Explicit expressions are obtained for particular cases involving su(2) and su(3) type fields, where the 3pt function can be written as a determinant. In the limit of large conformal weights of the operators, the 3pt function depends in a universal way of the three quasimomenta and the way they split into a left and right piece. "On the three-point functions of heavy non-BPS fields in N=4 SYM" Marius de Leeuw In this talk we present the RTT realization of the Yangian of centrally extended su(2|2). This formulation of the Yangian algebra elegantly packages all generators of the Yangian algebra and its Hopf algebra structure in the so-called T-matrix and the fundamental R-matrix. We will describe the unusual features that appear and explain how a braided coproduct naturally arises. We are also able to identify the secret symmetry of the R-matrix and extend it by defining additional secret symmetries at higher Yangian levels. "RTT realization of the AdS/CFT Yangian" Tristan McLoughlin The study of the world-sheet S-matrix for AdS_5 x S^5 strings was a key step in the complete determination of the spectrum of anomalous dimensions for planar N=4 super-Yang-Mills. To go beyond the spectral problem it is important to consider higher-point worldsheet correlation functions and, as is standard in many integrable models, one approach is the study of form factors. We will discuss the all-order functional equations that these objects must obey, their perturbative computation and their connection to four-dimensional gauge theory three-point functions. "World-sheet Form Factors in AdS/CFT" Olof Ohlsson Sax I will review the recent progress in understanding the worldsheet S-matrices of the massive sector of type IIB string theory on the backgrounds AdS_3xS^3xT^4 and AdS_3xS^3xS^3xS^1 using the symmetries of the spin-chains believed to describe the spectra of the dual conformal field theories. In particular I will discuss the supersymmetry algebra acting on the excitations and how this symmetry restricts the form of the S-matrix. The resulting S-matrices are determined up to some scalar factors known as dressing phases, which are further constrained by a set of crossing equations. I will show how we can obtain a solution to these equations in the T^4 case. Furthermore I will discuss the asymptotic Bethe ansatz equations obtained by diagonalizing the worldsheet S-matrix. "Worldsheet S-matrices for AdS3/CFT2" Paul Pearce An overview is given of the logarithmic minimal models (Pearce-Rasmussen-Zuber 2006) within a Yang-Baxter integrable approach to logarithmic CFT. The associated CFTs are introduced via a coset construction analogous to the coset construction of the rational minimal models. The characters and representation content of the chiral theories are reviewed in both the Virasoro and W-extended pictures. Conjectures for the modular invariant partition functions on the torus are also presented. Critical dense polymers and critical percolation are used throughout as the primary examples. "Logarithmic Minimal Models" Vasily Pestun I will describe the relation between the partition function of four-dimensional N=2 supersymmetric quiver gauge theoryin the omega background and the representation theory of quantum affine algebra, q-characters and quantum integrable systems. "From instanton functions to quantum groups" Jan Plefka We show that appropriately supersymmetrized smooth Wilson-Maldacena loop operators in N = 4 super Yang-Mills theory are invariant under a Yangian symmetry built upon the superconformal symmetry algebra psu(2, 2|4). The existence of the non-local symmetry is demonstrated at the one-loop order in the weak coupling limit as well as at leading order in the strong coupling limit employing the dual AdS5xS5 string description. The symmetry generators are non-local second order variational operators acting in the space of superloops. They yield a novel type of loop equation. Our findings represent the smooth counterpart to the Yangian invariance of scattering superamplitudes dual to light-like polygonal super Wilson loop in the N = 4 super Yang-Mills theory. "Yangian symmetry for smooth Maldacena-Wilson loops in N=4 SYM" Radu Roiban We shall review construction of the worldsheet S-matrix in AdS_n x S^n x M^(10-2n) spaces -- in particular of the dressing phase(s) -- at one and two loops through generalized unitarity. We shall also discuss a finite-coupling calculation of the energy of the long folded string through worldsheet methods. "Unitarity construction of worldsheet S-matrices in AdS_n x S^n x M" Christoph Sieg We show that in the non-supersymmetric gamma_i-deformation of N=4 SYM theory conformal invariance is broken by running double-trace couplings -- even in the 't Hooft limit. In the SU(2) subsector this breaking only affects the length L=2 operators. We demonstrate this explictly by reproducing for L>=3 the known leading finite-size corrections of the vacuum states from field theory. We identify a new type of finite-size correction that enters the L=2 results in the conformal beta- and the gamma_i-deformed theory. It should also be considered in the integrability-based approch, where divergences are encountered at L=2. "(Non-)conformality and finite-size effects in the gamma_i-deformation" Roberto Tateo The effective string theory describing the confining colour flux tube which joins a static quark-antiquark pair can be interpreted as a two-dimensional boundary conformal field theory perturbed by the bulk operator $T\bar{T}$ built with the components of the energy momentum tensor. This irrelevant perturbation is quantum integrable and the perturbed conformal field theory admits an exact scattering matrix description that yields, through the Thermodynamic Bethe Ansatz, the energy levels of the string which exactly coincide with the Nambu-Goto spectrum. (Based on the work [arXiv:1305.1278], in collaboration with M.Caselle, D.Fioravanti and F.Gliozzi.) "Nambu-Goto string and quark-antiquark potential from TBA" Jaroslav Trnka Recently, it was shown that on-shell scattering amplitudes in N=4 SYM can be calculated recursively using on-shell diagrams that are represented by integrals over the positive Grassmannian. In this talk we go further and show that scattering amplitudes in N=4 SYM can be understood as volumes of "The Amplituhedron", a natural generalization of convex polygons into the Grassmannian, extending the notion of positivity to a marriage between "internal" Grassmannian and "external" kinematical data. This invariant definition of the amplitude makes no reference to the usual concepts of quantum field theory. All fundamental properties of the amplitude, such as Unitarity, Locality and the Yangian symmetry, follow from positivity. "The Amplituhedron" Arkady Tseytlin We shall review recent work with Ben Hoare (arXiv:1303.1447 and arXiv:1304.4099) on massive sector of S-matrix of type IIB superstring theory AdS_3 x S^3 x T^4 background with mixed RR and NSNS 3-form fluxes. "S-matrix of AdS_3 x S^3 x T^4 superstring theory with RR and NSNS 3-form flux" Pedro Vieira In planar N=4 Super-Yang-Mills theory there is a map between gluons scattering amplitudes and null polygonal Wilson loops. This remarkable duality allows one to make an important step forward by Operator-Product-Expanding the scattering amplitudes. This action breaks down the four-dimensional amplitudes into a sequence of two-dimensional processes taking place on the flux tube sourced by the dual Wilson loops. In this talk I will outline how the integrable structures of the flux tube theory can be used for computing scattering amplitudes this way regardless of the value of the coupling. I will then present some weak coupling applications of the method. "Space-Time S-matrix and Flux-Tube S-matrix: Part I" Dmytro Volin In this talk we will introduce the quantum spectral curve, discuss its main properties and understand how it encodes the AdS/CFT spectrum. We will also take a look on some explicit results obtained from the quantum spectral curve. "Quantum spectral curve for AdS5/CFT4 spectral problem"