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Register a new userTidal excitation as mixing in thermal CFT
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We use mixed correlators in thermal CFT as clean probes of the strong gravity effects in their holographic duals. The dual interpretation of mixing is an inelastic conversion of one field to another field, induced by gravity: tidal excitation. We find an enhanced mixing at high temperatures, corresponding to large AdS black holes, concentrated to small boundary momenta, dual to the deep bulk, where strong gravitational fields are expected. We also find large $mathcal{O}(1/G_{N})$ tidal conversion in the low temperature phase of the $U(N)$ vector model, strengthening suspicions that the bulk dual of this phase also houses extremely compact objects.
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We study fermionic bulk fields in the dS/CFT dualities relating ${cal N}=2$ supersymmetric Euclidean vector models with reversed spin-statistics in three dimensions to supersymmetric Vasiliev theories in four-dimensional de Sitter space. These dualities specify the Hartle - Hawking wave function in terms of the partition function of deformations of the vector models. We evaluate this wave function in homogeneous minisuperspace models consisting of supersymmetry-breaking combinations of a half-integer spin field with either a scalar, a pseudoscalar or a metric squashing. The wave function appears to be well-behaved and globally peaked at or near the supersymmetric de Sitter vacuum, with a low amplitude for large deformations. Its behavior in the semiclassical limit qualitatively agrees with earlier bulk computations both for massless and massive fermionic fields.
We put forward new explicit realisations of dS/CFT that relate ${cal N}=2$ supersymmetric Euclidean vector models with reversed spin-statistics in three dimensions to specific supersymmetric Vasiliev theories in four-dimensional de Sitter space. The partition function of the free supersymmetric vector model deformed by a range of low spin deformations that preserve supersymmetry appears to specify a well-defined wave function with asymptotic de Sitter boundary conditions in the bulk. In particular we find the wave function is globally peaked at undeformed de Sitter space, with a low amplitude for strong deformations. This suggests that supersymmetric de Sitter space is stable in higher-spin gravity and in particular free from ghosts. We speculate this is a limiting case of the de Sitter realizations in exotic string theories.
The tools of Kerr/CFT correspondence are applied to the Kerr black hole embedded in an axial external magnetic field. Its extremal near horizon geometry remains a warped and twisted product of $AdS_2times S^2$. The central charge of the Virasoro algebra, generating the asymptotic symmetries of the near horizon geometry, is found. It is used to reproduce, via the Cardy formula, the Bekenstein-Hawking entropy of the magnetised Kerr black hole as the statistical microscopic entropy of a dual CFT. The presence of the background magnetic field makes available also a second dual CFT picture, based on the $U(1)$ electromagnetic symmetry, instead of the only rotational one of the standard non-magnetised Kerr spacetime. A Meissner-like effect, where at extremality the external magnetic field is expelled out of the black hole, allows us to infer the value of the mass for these magnetised extremal black holes. The generalisation to the CFT dual for the magnetised extreme Kerr-Newman black hole is also presented.
This is a status report on a research program aimed at obtaining quantum-gravitational physics inside a cosmological horizon through dS/CFT, i.e. through a holographic description at past/future infinity of de Sitter space. The program aims to bring together two main elements. The first is the observation by Anninos, Hartman and Strominger that Vasilievs higher-spin gravity provides a working model for dS/CFT in 3+1 dimensions. The second is the proposal by Parikh, Savonije and Verlinde that dS/CFT may prove more tractable if one works in so-called elliptic de Sitter space - a folded-in-half version of global de Sitter where antipodal points have been identified. We review some relevant progress concerning quantum field theory on elliptic de Sitter space, higher-spin gravity and its holographic duality with a free vector model. We present our reasons for optimism that the approach outlined here will lead to a full holographic description of quantum (higher-spin) gravity in the causal patch of a de Sitter observer.
We present a new exact black hole solution in three dimensional Einstein gravity coupled to a single scalar field. This is one of the extended solutions of the BTZ black hole and has in fact $textrm{AdS}_3$ geometries both at the spatial infinity and at the event horizon. An explicit derivation of Virasoro algebras for $textrm{CFT}_2$ at the two boundaries is shown to be possible `{a} la Brown and Henneauxs calculation. If we regard the scalar field as a running coupling in the dual two dimensional field theory, and its flow in the bulk as the holographic renormalization group flow, our black hole should interpolate the two $textrm{CFT}_2$ living at the infinity and at the horizon. Following the Hamilton-Jacobi analysis by de Boer, Verlinde and Verlinde, we calculate the central charges $c_{textrm{UV}}$ and $c_{textrm{IR}}$ for the $textrm{CFT}_2$ on the infinity and the horizon, respectively. We also confirm that the inequality $c_{textrm{IR}} < c_{textrm{UV}}$ is satisfied, which is consistent with the Zamolodchikovs c-theorem.
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