In its most general formulation the gauge/string duality may be used to build models of various strongly coupled systems in condensed matter. One of these is high-temperature d-wave superconductor. The holographic model of d-wave superconductor includes the dynamics of spin-2 charged field on top of the curved AdS geometry. In the probe approximation the model may be formulated consistently and exhibits a number of interesting physical phenomena. The important task is to classify all possible ground states of the model, which will correspond to the various phases of the dual system, and study the resulting phase diagram. In this talk I will discuss the recently found ground state which exhibits the stripes of charge density, violates the translation symmetry spontaneously and may be associated with the pseudogap state in high-Tc superconductors.

Abelian gerbes play a ubiquitous role in string and supergravity theories. It is conjectured that non-abelian gerbe theories exist, but a satisfactory explicit construction of such a theory has not yet been achieved. Inspired by the possibility that a non-abelian theory of gerbes may be possible on non-conventional spacetimes, I will consider a toy model on a lattice that allows one to make some progress in this problem. In this talk, I will show how abelian gerbe theories may be described naturally on the lattice. I will outline a non-abelian generalisation and show how, under dimensional reduction, such theories give rise to lattice Yang-Mills.

Starting from some examples, I will review various implications of classical consistency that have played a key role in the context of higher-spin theories (Vasiliev's equations) and holography. I will then review the current understanding higher-spin interactions involving totally-symmetric higher-spin fields and the associated classification of higher-spin algebras generalizing Coleman-Mandula theorem in the context of AdS/CFT. Finally, I will discuss the extension of this analysis to massive higher spins, towards a new understanding of string theory.

I will present this very recently proposed geometric object, conjectured to give the N=4 SYM scattering amplitudes at all orders, and illustrate the techniques used to fully explore its structure. In so doing I will give firm nontrivial evidence to the amplituhedron conjecture.

The algebras of higher spin symmetries in conformal field theories in four and six dimensions are not unique and have a richer structure due to the existence of infinite short multiplets besides the usual scalar and spinor. We will focus on recent results that show there exists a one parameter family (continuous of d=4 and discrete for d=6) of higher spin algebras and superalgebras, and give an explicit unitary representation for these algebras using quasiconformal methods. We will also discuss the implications of these results for the AdS5/CFT4 and AdS7/CFT6 higher spin holography.

In recent years, due to the method of supersymmetric localization, many exact results have been achieved in the study of supersymmetric gauge theories on compact spaces of various dimension and topology, leading to the discovery of surpraising structures. An important example is provided by the correspondence introduced by Alday, Gaiotto and Tachikawa, relating the partition functions of a large class of supersymmetric gauge theories on S4 and S2 to correlators in Liouville CFT. In this talk, I will explain how this picture can be lifted to higher dimensional gauge theories via the correspondence of partition functions on S5, S4xS1, S3 and S2xS1 to correlators in theories whose underlying symmetry is given by a quantum deformation of the Virasoro algebra. In particular, I will discuss how 3-point functions can be derived by the bootstrap approach and used to define this novel class of q-deformed CFTs. I will also discuss some aspects related to integrable structures in these models, such as reflection coefficients, as well as possible generalisation.

Within the context of the duality between higher spin gravitational theories and a semi- classical limit of W_N minimal models, we consider 2D CFTs with W_∞ symmetry at finite temperature, deformed by the presence of a chemical potential for the spin–three current. As a perturbative expansion in the chemical potential, we compute the Renyi and entanglement entropies for a single interval. The leading correction is universal and matches the holographic result, based on Wilson line functionals, obtained from the higher spin gravitational dual.

It will be shown how supersymmetry and superalgebras arise in lattice models both in one and higher dimensions. Examples using correlated fermions and bosons will be primarily used. Some of the examples will have associated superalgebras and others will have supersymmetry more commonly used in field theory. Some aspects of continuum limits will also be touched upon.

I will show that the non-stringy holographic description of hadrons, namely the one based on fields that reside on the bulk and flavor branes, fails to reproduce the hadronic spectra. I will briefly review the stringy duals of Wilson loops and determine the sufficient conditions of confining backgrounds. I will show that the latter are also the requirements for holographic stringy mesons to admit a Regge-like spectrum. I will determine a map between holographic stringy mesons and strings with massive endpoints in 4d flat space-time. Models of classical rotating strings with massive endpoints will be written down. I will discuss the (still unsolved) quantization of such systems. Fits of the models to mesonic data will be presented. A universal model that describes mesons of u,d,s,c quarks will be developed. Mesons with b quarks will also be fitted. I will describe the construction of stringy baryons in holography. I will show that the best description of baryons is in terms of a single string with a quark and a di-quark on its ends. I will present fits of such a model to the baryonic data. Finally I will describe the stringy decays of holographic hadrons.

In this talk we will try to motivate why the study of the Regge limit in a correlation function of a conformal field theory is interesting. We will review the results obtained in the past few years and present some on going work in phi^3 theory using skeleton expansion.

I will show how to construct the familiar heterotic NS5 brane as a topological soliton in a supercritical version of heterotic string theory. Closed string tachyon condensation removes the extra dimensions, leaving the NS5 in 10d, in a process highly reminiscent of the K-theoretical description of type II D-branes, but linking non-trivial gauge bundles and geometry. The construction requires a modification of the anomalous Bianchi identity for H_3 in supercritical heterotic string theory. I will give various proofs for the existence of this modification.

We study geometric aspects and holomorphic properties of N = (0, 2) Heterotic Sigma Models over symmetric spaces, and derive a number of exact relations for the β functions in terms of the analogy to the NSVZ β function in four-dimensional Yang-Mills. We will show that in spite of the heterotic nature, the isometries are preserved at the quantum level. We will also discuss the N = (0, 2) supercurrent multiplet (the so-called hypercurrent) and its anomalies, as well as the “Konishi anomaly.” This gives us another method for finding two-loop β functions. The talk is based on joint work with J. Chen, M. Shifman and A. Vainshtein.

We systematically analyze a broad class of dual heterotic and F-theory models that give four-dimensional supergravity theories, and compare the geometric constraints on the two sides of the duality. In this talk I will show that F-theory gives new insight into the conditions under which heterotic vector bundles can be constructed. We show that in many cases the F-theory geometry imposes a constraint on the extent to which the gauge group can be enhanced, corresponding to limits on the way in which the heterotic bundle can decompose. We explicitly construct all dual F-theory/heterotic pairs in the class under consideration where the common twofold base surface is toric, and give both toric and non-toric examples of the general results. Finally, we provide evidence for important new aspects of G-flux in four-dimensional compactifications.

Motivated by the search for new backgrounds with solvable string theories, the talk classifies the D-brane geometries leading to integrable geodesics. This analysis gives severe restrictions on the potential candidates for integrable string theories. It is demonstrated that the Hamilton-Jacobi equation for massless geodesics can only separate in elliptic or spherical coordinates, all known integrable backgrounds are covered by this separation, and new examples are constructed. The Killing and Killing-Yano tensors associated with such separation and their transformations under string dualities are also discussed.

I will discuss the Maldacena-Lewkowycz derivation of the Ryu-Takayangi prescrition for holographic entanglement entropy, and extend it to a more general class of theories of gravity in the bulk. This analysis results in a new euclidean entropy functional, that generalises Wald's entropy. In lorentzian signature, this functional is a natural extension of Wald's black hole entropy to time dependent situations.