Abstract : We study the effective potentials for various probe branes surrounding AdS4 black holes with massive halos in consistent truncations of M-theory on the Sasaki-Einstein7 manifolds Q111 and M111. These probes are either M2 branes extended in spacetime or “particle-like” probes such as internally wrapped M2 branes and, upon reduction to type IIA String theory, D6 branes corresponding to baryon operators in the dual Chern-Simons theory. We find both global and local minima of the potential outside the horizon, indicating the existence of stable and metastable multicenter AdS black holes in the extreme mass ratio regime, at fixed temperature and charges. For the planar case, we also find an instability towards nucleation of spacetime-filling M2 branes. With this analysis, we address some open questions on the holographic description of glassy phases of matter.

We use the variational principle approach to derive the large NN holographic dictionary for two-dimen-sional T\bar TTT‾-deformed CFTs, for both signs of the deformation parameter. The resulting dual gravitational theory has mixed boundary conditions for the non-dynamical graviton; the boundary conditions for matter fields are undeformed. When the matter fields are turned off and the deformation parameter is negative, the mixed boundary conditions for the metric at infinity can be reinterpreted on-shell as Dirichlet boundary conditions at finite bulk radius, in agreement with a previous proposal by McGough, Mezei and Verlinde. The holographic stress tensor of the deformed CFT is fixed by the variational principle, and in pure gravity it coincides with the Brown-York stress tensor on the radial bulk slice with a particular cosmological constant counterterm contribution. In presence of matter fields, the connection between the mixed boundary conditions and the radial ``bulk cutoff’’ is lost. Only the former correctly reproduce the energy of the bulk configuration, as expected from the fact that a universal formula for the deformed energy can only depend on the universal asymptotics of the bulk solution, rather than the details of its interior. The asymptotic symmetry group associated with the mixed boundary conditions consists of two commuting copies of a state-dependent Virasoro algebra, with the same central extension as in the original CFT.

We show that T\bar{T}, J\bar{T}TT‾,JT‾ and JT_aJTa - deformed classical CFTs posses an infinite set of symmetries that take the form of a field-dependent generalization of two-dimensional conformal transformations. If, in addition, the seed CFTs possess an affine U(1)U(1) symmetry, we show that it also survives in the deformed theories, again in a field-dependent form. These symmetries can be understood as the infinitely-extended conformal and U(1)U(1) symmetries of the underlying two-dimensional CFT, seen through the prism of the ``dynamical coordinates’’ that characterise each of these deformations. We also compute the Poisson bracket algebra of the associated conserved charges, using the Hamiltonian formalism. In the case of the J\bar{T}JT‾ and JT_{a}JTa deformations, we find two copies of a functional Witt - Kac-Moody algebra. In the case of the T\bar{T}TT‾ deformation, we show that it is also possible to obtain two commuting copies of the Witt algebra.

Pure gravity in AdS3 is a theory of boundary excitations, most simply expressed as a constrained free scalar with an improved stress tensor that is needed to match the Brown-Henneaux central charge. Excising a finite part of AdS gives rise to a static gauge Nambu-Goto action for the boundary graviton. We show that this is the TT¯ deformation of the infinite volume theory, as the effect of the improvement term on the deformed action can be absorbed into a field redefinition. The classical gravitational stress tensor is reproduced order by order by the TT¯ trace equation. We calculate the finite volume energy spectrum in static gauge and find that the trace equation imposes sufficient constraints on the ordering ambiguities to guarantee agreement with the light-cone gauge prediction. The correlation functions, however, are not completely fixed by the trace equation. We show how both the gravitational action and the TT¯ deformation allow for finite improvement terms, and we match these to the undetermined total derivative terms in Zamolodchikov’s point splitting definition of the TT¯ operator.

The quantization of pure 3D gravity with Dirichlet boundary conditions on a finite boundary is of interest both as a model of quantum gravity in which one can compute quantities which are ``more local" than S-matrices or asymptotic boundary correlators, and for its proposed holographic duality to T\overline{T}TT¯-deformed CFTs. In this work we apply covariant phase space methods to deduce the Poisson bracket algebra of boundary observables. The result is a one-parameter nonlinear deformation of the usual Virasoro algebra of asymptotically AdS_33 gravity. This algebra should be obeyed by the stress tensor in any T\overline{T}TT¯-deformed holographic CFT. We next initiate quantization of this system within the general framework of coadjoint orbits, obtaining — in perturbation theory — a deformed version of the Alekseev-Shatashvili symplectic form and its associated geometric action. The resulting energy spectrum is consistent with the expected spectrum of T\overline{T}TT¯-deformed theories, although we only carry out the explicit comparison to \mathcal{O}(1/\sqrt{c})𝒪(1/c) in the 1/c1/c expansion.

We develop a new hybrid WKB technique to compute boundary-to-boundary scalar Green functions in asymptotically-AdS backgrounds in which the scalar wave equation is separable and is explicitly solvable in the asymptotic region. We apply this technique to a family of six-dimensional \frac{1}{8}18-BPS asymptotically AdS_3\,\times\,3×S^33 horizonless geometries that have the same charges and angular momenta as a D1-D5-P black hole with a large horizon area. At large and intermediate distances, these geometries very closely approximate the extremal-BTZ\,\times\,×S^33 geometry of the black hole, but instead of having an event horizon, these geometries have a smooth highly-redshifted global-AdS_3\,\times\,3×S^33 cap in the IR. We show that the response function of a scalar probe, in momentum space, is essentially given by the pole structure of the highly-redshifted global-AdS_33 modulated by the BTZ response function. In position space, this translates into a sharp exponential black-hole-like decay for times shorter than N_1 N_5N1N5, followed by the emergence of evenly spaced “echoes from the cap,” with period \sim N_1 N_5∼N1N5. Our result shows that horizonless microstate geometries can have the same thermal decay as black holes without the associated information loss.

Abstract : We propose a complete microscopic definition of the Hilbert space of minimal higher spin de Sitter quantum gravity and its Hartle-Hawking vacuum state. The funda- mental degrees of freedom are 2N bosonic fields living on the future conformal boundary, where N is proportional to the de Sitter horizon entropy. The vacuum state is normalizable. The model agrees in perturbation theory with expectations from a previously proposed dS- CFT description in terms of a fermionic Sp(N) model, but it goes beyond this, both in its conceptual scope and in its computational power. In particular it resolves the apparent pathologies affecting the Sp(N) model, and it provides an exact formula for late time vac- uum correlation functions. We illustrate this by computing probabilities for arbitrarily large field excursions, and by giving fully explicit examples of vacuum 3- and 4-point functions. We discuss bulk reconstruction and show the perturbative bulk QFT canonical commuta- tions relations can be reproduced from the fundamental operator algebra, but only up to a minimal error term ∼ e −O(N ), and only if the operators are coarse grained in such a way that the number of accessible “pixels” is less than O(N ). Independent of this, we show that upon gauging the higher spin symmetry group, one is left with 2N physical degrees of freedom, and that all gauge invariant quantities can be computed by a 2N × 2N matrix model. This suggests a concrete realization of the idea of cosmological complementarity.