Half BPS states (operators) in N=4 SYM are famously described by free fermions both at weak and strong coupling. I describe a set of conjectures for a preferred class of states in more general conformal field theories that can be tested in supergravity for when such a free fermion description might arise and some motivation for it applying generally. The states in question belong to the chiral ring of a supersymmetric conformal field theory that extremize an additional U(1) charge for fixed dimension and can be reduced to multi-traces of a composite matrix field, which is equivalent to using Young tableaux (Schur polynomials) as a basis. The main conjecture asserts that if the Young tableaux are orthogonal, then the set of extremal three point functions of traces to order 1/N are determined up to a single constant. The conjecture is extended further by providing an exact norm for the Schur basis and this norm arises from a set of free fermions for a generalized oscillator algebra.

My starting point is a holographic model of the Kondo effect recently proposed by Erdmenger et. al., i.e. of a magnetic impurity interacting with a strongly coupled system. Specifically, I focus on the challenges of computing gravitational backreaction in this model, which demands a study of the Israel junction conditions. I present general results on these junction conditions, including analytical solutions for certain toy models, that may be relevant also more generally in the AdS/boundary CFT correspondence. Furthermore, similar junction conditions for a bulk Chern-Simons field appearing in the holographic Kondo model are discussed. I then focus on the computation and interpretation of entanglement entropy in this holographic model.

I will discuss how to construct rigid supersymmetric gauge theories on Riemannian five-manifolds following a holographic approach. This approach realises the five-manifold as the conformal boundary of a six-dimensional bulk supergravity solution and leads to a systematic classification of five-dimensional supersymmetric backgrounds with gravity duals. The background metric is furnished with a conformal Killing vector, which generates a transversely holomorphic foliation with a transverse Hermitian structure. Finally, I’ll also construct supersymmetric Lagrangians for gauge theories coupled to arbitrary matter on such backgrounds.

I will discuss the partition function of 4d N=1 theories on Hopf surfaces. These are diffeomorphic to S^1 x S^3 and the partition function provides a path integral realization of the supersymmetric index. Its large S^1 limit exhibits a universal behaviour associated to the existence of a Casimir energy. I will argue that, contrarily to the non-supersymmetric case, this Casimir energy is a physical (non-ambiguous) quantity in supersymmetric theories.

In this talk I will discuss how to construct all solutions consistent with crossing symmetry in the limit of large central charge c ~ N^2, starting from the four-point correlator of the stress tensor multiplet in N=4 SYM. Unitarity forces the introduction of a scale \Delta_{gap} and these solutions organize as a double expansion in 1/c and 1/\Delta_{gap}. These solutions are valid to leading order in 1/c and to all orders in 1/\Delta_{gap} and reproduce, in particular, instanton corrections previously found. Comparison with such instanton computations allows to fix \Delta_{gap}. Using this gap scale one can explain the upper bounds for the scaling dimension of unprotected operators observed in the numerical superconformal bootstrap at large central charge.

Supergravity theories were once hoped to provide ultraviolet finite theories of quantum gravity without requiring profoundly new physical frameworks. These hopes faded in the 1980s, but renewed efforts in recent years have uncovered some surprising ultraviolet behaviour. In this talk, I will give an overview of the explicit scattering amplitude calculations in perturbative supergravity over the last few years. In particular cases, there are indications of ultraviolet cancellations not accounted for by known symmetry arguments. I will highlight these cases and give some reasons to be optimistic and some reasons to be pessimistic about supergravity as a contender for a quantum theory of gravity.

We review the construction of the so-called λ-deformations of WZW and gauged WZW models. We discuss their integrability and algebraic properties, their behavior under RG flows as well as their embeddings to type-II supergravity.

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.