The singleton deformation of Higher-Spin gauge theory and the phase structure of the three-dimensional O(N) Vector Model

We consider a singleton deformation of the AdS the three-dimensional O(N) vector model. The singleton couples to the higher-spin multiplet only through a marginal boundary interaction. We argue that the effect of such a deformation is to shift N -> N+ 1 in both sides of the holographic correspondence and we show how the gap equations of the three-dimensional O(N) vector model arise from the higher-spin theory. The singleton deformation breaks higher-spin symmetry and gives rise to the well-known 1/N anomalous dimensions of the boundary theory.

Background solutions of topologically gauged CFT´s in three dimensions

After a short introduction to ABJM and BLG theories I will review the gauging of their global symmetries, i.e. the construction of the corresponding topologically gauged versions. These gauged theories contain new sixth order potentials for the scalar fields which lead to a number of background solutions whose properties we will briefly review. Some other special properties of these theories like the possibility of a sequential AdS/CFT will also be discussed.

Black Holes, General Relativity and Thermodynamics

It is now claimed that Black Holes exist! I shall review some of the evidence, briefly, and then talk about the larger problem of identifying the sources of the gravitational metric. The much used procedure proposed by Tolman leaves much room for improvement. The case of a mass distribution based one or more scalar density fields is already developed and integrated with thermodynamics. Next in importance is the case of strong electromagnetic fields and the photon gas. The problem of quantized gravity takes on a different aspect.

Black holes in 3 dimensions

Black holes are ideal laboratories for theories of gravity. This talk will focus on some black hole solutions in three dimensional higher spin gravity. First I will review how these black holes are constructed. Several groups investigated the thermal dynamical quantities, and showed that the laws of thermal dynamics are obeyed. Discrepancies, however, occur due to different approaches to the problem. In the last part of the talk, I will show how to understand these discrepancies by a careful analysis of the asymptotic symmetry group.

Gravitational flat space holography in 3 dimensions

In the limit where the cosmological radius goes to infinity, there are interesting cosmological solutions in three dimensions whose horizon is the remnant of the inner horizon of the BTZ black holes. After briefly discussing a symmetry based derivation of their entropy, I will construct the dual boundary theory for three-dimensional asymptotically flat Einstein gravity at null infinity by starting from the Chern-Simons formulation in the bulk.

Review of Double Field Theory

I review double field theory, with an emphasis on the (doubled) generalized spacetime and the notion of generalized coordinate transformations. These transformations unify conventional diffeomorphisms and b-field gauge trabsformations, but also encode the T-duality group O(d,d) for toroidal backgrounds.

New approach to self-dual nonlinear electrodynamics

We present a new off-shell formulation of the self-dual nonlinear electrodynamics models involving tensorial auxiliary fields. The Gaillard-Zumino self-duality constraint and duality transformations are linearized in this approach. We focus on the U(1) duality-invariant models including the Born-Infeld one. The analogous reformulation exists for the general case of $U(N)$ duality, as well as for self-dual models of N=1 and N=2 supersymmetric electrodynamics.

Higher order singletons, partially massless fields and their boundary values in the ambient approach

Using ambient space we develop a fully gauge-covariant approach to boundary values of AdS gauge fields. The approach is employed in studying (partially) massless fields in the bulk and higher-order conformal scalars (singletons) as well as (generalized) Fradkin--Tseytlin fields on its boundary. In particular, we identify (generalized) Fradkin--Tseytlin equations as obstructions in extending the off-shell boundary value to the bulk. These can also be seen as the partially massless generalizations of the usual holographic anomaly known in the literature. We also relate the background fields for the higher order singleton to boundary values of partially massless fields in the bulk and prove the appropriate generalization of the Flato--Fronsdal theorem. The relation is in agreement with the known structure of the higher symmetries of the singleton.

Local cubic vertex functions for three massless higher even spin fields on spaces AdS(D): An analytic approach

Local cubic vertex functions of three higher even spin fields on AdS(D) are constructed from the Green function of three conserved currents that are dual to the higher spin fields. Conservation of the currents implies lowest order gauge invariance. These vertex functions appear by the UV-divergence as the residue of the highest order pole in the dimensional regularization parameter \epsilon. In fact N-point Green functions of such conserved currents produce a series of poles up to the order N-1. The method works for even space-time dimensions and maintains covariance at any step. The resulting formula is quite concise.

BRST field theory for continuous spin

Some puzzling aspects of higher spin field theory in Minkowski space-time, such as the tracelessness constraints and the search for an underlying physical principle, will be discussed. A connecting idea might be provided by the continuous spin representations of the Poincar´e group. The Wigner equations, treated as first class constraints, yields to a four-constraint BRST formulation. The resulting field theory generalizes free higher spin field theory. A simple analysis of the constraint structure reveals a hint of a physical rationale behind the trace constraints.

Gauge algebra, involution, and consistent interactions.

The talk reviews some of the recent developments in general gauge field theory. The reviewed issues include the BRST complex, covariant quantisation, symmetries and conservation laws in not necessarily Lagrangian gauge theories. A particular attention is devoted to the concept of involutive closure of field equations. Starting with the involutive form of the field equations, a universal method is proposed for constructing consistent interactions between the fields. The method equally well applies to the Lagrangian and non-Lagrangian equations and it is explicitly covariant. The equations may have (or have no) gauge symmetry and/or second class constraints in Hamiltonian formalism. In every case the method identifies all the consistent interactions.

On spin-2 and 3 gauge theory in AdS background

A new view on the construction of interacting higher spin theories is proposed. The connection with the previously studied constructions is considered.

Mixed-symmetry tensor conserved currents and AdS/CFT correspondence

We present the full list of conserved currents that exactly matches the spectrum of AdS mixed-symmetry fields arising in the generalized Flato-Fronsdal theorem for two spinor singletons.

BRST-BFV procedure for the construction of gauge invariant Lagrangians for symmetric and mixed-symmetry higher-spin fields

I plan to discuss the construction of gauge-invariant Lagrangian formulations both for unconstrained and constrained higher-spin fields in d-dimensional constant curvature space-times starting from the realization of initial Poincare or anti-de-Sitter group irreducible conditions on tensors or spin-tensors in terms of the constraints on stringy-inspired Hilbert space. We start from the simple case of totally-symmetric higher-spin fields in the metric-like formalism on Minkowski and AdS spaces and then extend the results to arbitrary (bosonic and fermionic) mixed-symmetry HS fields. The peculiarities of higher-spin (cubic vertex) interactions within the BRST-BFV approach are shortly discussed. The comparison with frame-like formulations are considered as well.

Worldline approach to higher spin fields on (A)dS and quantum gravity

I describe a first-quantized approach to a class of higher spin fields which make use of spinning particle models with extended supersymmetry on their worldline. I describe how this gives a useful parametrization of the corresponding one-loop effective action on (A)dS spaces, and indicate how to compute the first few heat kernel coefficients (i.e. the diverging terms in D=4). Finally, I comment on a different worldline realization of the spin 2 particle in D=4.

Three-dimensional Massive Gravity

In this talk I discuss gravity in three spacetime dimensions and its massive extensions. I will review some old and discuss some new developments, including the recent New Massive Gravity model.

Wilson Lines and Entanglement in Higher Spin Theories

The characteristic feature of higher spin theories is the lack of a geometric interpretation of the fields beyond the perturbative level, which leaves unclear how to probe global features of a solution. In this talk we will discuss how to construct the appropriate observable that will measure entanglement for higher spin gravity. We will construct a probe---with the aim to generalize geodesic distances---for higher spin theories and we will argue that the Wilson line is the correct probe of the geometry. This observable achieves the same goal as a geodesic for pure AdS gravity, in that the probe will report back a number which is the proper distance in the bulk. For higher spin gravity this topological probe gives new predictions in the context of AdS/CFT.