We will present new AdS_6 and AdS_4 backgrounds constructed using non-Abelian T-duality on known solutions and discuss some properties of the dual CFTs associated to these backgrounds.

I'll revisit some old of ideas of Euclidean quantum gravity, in which manifolds of different topology are summed in the path integral. I'll show that, in certain circumstances, gravitational instantons can destabilise supersymmetric Kaluza-Klein compactifications. We'll also see how one-loop divergences in quantum gravity can be subsumed into a new RG-invariant topological scale.

The S-matrix of the world-sheet theory of the string in AdS(5)xS(5) is known to admit a deformation where the original symmetry algebra is replaced by the associated quantum group. The case where q, the deformation parameter, is real has been identified as a particular deformation of the Green-Schwarz sigma model known as the "eta-deformation". The case with q a root of unity interpolates between the AdS(5)xS(5) world-sheet theory and its Pohlmeyer reduction. However, an interpretation of this case is still lacking. We will summarize recent work aimed to show that sigma models on (semi-)symmetric spaces F/G admit discrete integrable deformations that can be viewed as deformations of the F/F gauged WZW model. For the AdS(5)xS(5) world-sheet theory, F=PSU(2,2|4) and the resulting theory has just the right amount of kappa-symmetries, which points to the existence of a new fully consistent deformed string background.

We will discuss the relation between perturbative gauge theory and perturbative gravity, and look at how this relation extends to some exact classical solutions. First, we will review the double copy prescription that takes gauge theory amplitudes into gravity amplitudes, which has been crucial to progress in perturbative studies of supergravity. Then, we will see that the self-dual sectors provide an important insight into the relation between the theories. A key role is played by a kinematic algebraic structure mirroring the colour structure. Finally, we will see how these ideas extend to some exact classical solutions, namely black holes and plane waves. This leads to a relation of the type Schwarzschild as Coulomb charge squared.

I will review the calculation of the partition function of 3d supersymmetric field theories on S^3 using the fermi-gas approach to solve the matrix integral. The resulting expression is an Airy function and is valid perturbatively to all orders in 1/N for a wide class of theories (including ABJM). This suggests that a similar formula can be derived by studying quantum gravity on AdS_4. I will explain several of the steps needed to implement this idea and some intriguing results.

TBA

In my talk I will give a brief review on entanglement entropy and discuss some recent developments which include relations to the geometric Willmore conjecture and the role of total derivatives in the trace anomaly.

It will be shown that the dynamics of discrete (integer-valued) Hamiltonian cellular automata can only be consistently defined, if it is linear in the same sense that unitary evolution in quantum mechanics is linear. This suggests us to look for an invertible map between such automata and continuous quantum mechanical models. Based on sampling theory, such a map can indeed be constructed and leads to quantum mechanical models which incorporate a fundamental scale. The admissible observables, the one-to-one correspondence of the respective conservation laws, and the existence of solutions of the modified dispersion relation for stationary states are discussed. References: H.-T. Elze, Action principle for cellular automata and the linearity of quantum mechanics, Phys. Rev. A 89, 012111 (2014) [arXiv:1312.1615]; do., Journal of Physics: Conference Series 504 (2014) 012004 [arXiv:1403.2646];

It is widely believed that hydrodynamics is the low energy effective theory of any quantum field theory. In this talk I will derive the local low energy effective action for uncharged dissipationless conformal fluids through holography. This can be achieved by solving a double-Dirichlet problem for linearised gravitational perturbations between the conformal boundary of a (4+1)-dimensional AdS-black brane background and a stretched horizon. Interestingly dissipationless fluid dynamics is captured by Goldstone bosons of the broken symmetries by the classical solution ending on the second boundary. I will discuss how the effective action approach might be inconsistent unless there is a coupling to a dissipative dynamical IR sector which for simplicity can be replaced by a membrane paradigm-like boundary condition on a stretched horizon and I will also comment on the limits of validity of this simplification.

We determine the most general three-dimensional vacuum spacetime with a negative cosmological constant containing a non-singular Killing horizon. We show that the general solution with a spatially compact horizon possesses a second commuting Killing field and deduce that it must be related to the BTZ black hole (or its near-horizon geometry) by a diffeomorphism. We show there is a general class of asymptotically AdS_3 extreme black holes with arbitrary charges with respect to one of the asymptotic-symmetry Virasoro algebras and vanishing charges with respect to the other. We interpret these as descendants of the extreme BTZ black hole.

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.