October 18, 2011
We investigate higher spin theories of gravity in three dimensions based on the gauge group SL(N,R)*SL(N,R). In these theories the usual diffeomorphism symmetry is enhanced to include higher spin gauge transformations under which traditional geometric notions of curvature and causality are no longer invariant. This implies, for example, that apparently singular geometries can be rendered smooth by a gauge transformation, much like the resolution of orbifold singularities in string theory. The classical solutions, including the recently constructed higher spin black hole, are characterized by their holonomies around the non-contractible cycles of space-time. The black hole solutions are shown to be gauge equivalent to a BTZ black hole which is charged under a set of U(1) Chern-Simons fields. Nevertheless, depending on the choice of embedding of the gravitational gauge group, the space-time geometry may be non-trivial. We study in detail the N=3 example, where this observation allows us to find a gauge where the black hole geometry takes a simple form and the thermodynamic properties can be studied.
Similar papers 1
June 23, 2011
Higher spin gravity is an interesting toy model of stringy geometry. Particularly intriguing is the presence of higher spin gauge transformations that redefine notions of invariance in gravity: the existence of event horizons and singularities in the metric become gauge dependent. In previous work, solutions of spin-3 gravity in the SL(3,R) x SL(3,R) Chern-Simons formulation were found, and were proposed to play the role of black holes. However, in the gauge employed there, t...
February 6, 2014
We review some relevant results in the context of higher spin black holes in three-dimensional spacetimes, focusing on their asymptotic behaviour and thermodynamic properties. For simplicity, we mainly discuss the case of gravity nonminimally coupled to spin-3 fields, being nonperturbatively described by a Chern-Simons theory of two independent sl(3,R) gauge fields. Since the analysis is particularly transparent in the Hamiltonian formalism, we provide a concise discussion of...
March 22, 2011
We study classical solutions of three dimensional higher spin gravity in the Chern-Simons formulation. We find solutions that generalize the BTZ black hole and carry spin-3 charge. The black hole entropy formula yields a result for the asymptotic growth of the partition function at finite spin-3 chemical potential. Along the way, we develop technology for computing AdS/CFT correlation functions involving higher spin operators.
August 26, 2012
We review recent progress in the construction of black holes in three dimensional higher spin gravity theories. Starting from spin-3 gravity and working our way toward the theory of an infinite tower of higher spins coupled to matter, we show how to harness higher spin gauge invariance to consistently generalize familiar notions of black holes. We review the construction of black holes with conserved higher spin charges and the computation of their partition functions to lead...
April 23, 2012
In the context of (2+1)--dimensional Chern-Simons SL(N,R)\times SL(N,R) gauge fields and spin N black holes we compute the on-shell action and show that it generates sensible and consistent thermodynamics. In particular, the Chern-Simons action solves the integrability conditions recently considered in the literature.
November 30, 2015
The gauge sector of three-dimensional higher spin gravities can be formulated as a Chern-Simons theory. In this context, a higher spin black hole corresponds to a flat connection with suitable holonomy (smoothness) conditions which are consistent with the properties of a generalized thermal ensemble. Building on these ideas, we discuss a definition of black hole extremality which is appropriate to the topological character of 3d higher spin theories. Our definition can be phr...
September 4, 2013
We study the resolution of certain cosmological singularity in the context of higher-spin three-dimensional gravity. We consider gravity coupled to a spin-3 field realized as Chern-Simons theory with gauge group $SL(3,\mathbb{C})$. In this context we elaborate and extend a singularity resolution scheme proposed by Krishnan and Roy. We discuss the resolution of a big-bang singularity in the case of gravity coupled to a spin-4 field realized as Chern-Simons theory with gauge gr...
April 12, 2014
Three-dimensional spacetime with a negative cosmological constant has proven to be a remarkably fertile ground for the study of gravity and higher spin fields. The theory is topological and, since there are no propagating field degrees of freedom, the asymptotic symmetries become all the more crucial. For pure (2+1) gravity they consist of two copies of the Virasoro algebra. There exists a black hole which may be endowed with all the corresponding charges. The pure (2+1) grav...
February 4, 2013
We discuss the thermodynamics of recently constructed three-dimensional higher spin black holes in SL(N,R)\times SL(N,R) Chern-Simons theory with generalized asymptotically-anti-de Sitter boundary conditions. From a holographic perspective, these bulk theories are dual to two-dimensional CFTs with W_N symmetry algebras, and the black hole solutions are dual to thermal states with higher spin chemical potentials and charges turned on. Because the notion of horizon area is not ...
October 2, 2013
We study asymptotically Lifshitz solutions to three dimensional higher spin gravity in the SL(3,R)xSL(3,R) Chern-Simons formulation. We begin by specifying the most general connections satisfying Lifshitz boundary conditions, and we verify that their algebra of symmetries contains a Lifshitz sub-algebra. We then exhibit connections that can be viewed as higher spin Lifshitz black holes. We show that when suitable holonomy conditions are imposed, these black holes obey sensibl...