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Spacetime geometry in higher spin gravity. (English) Zbl 1303.83019

Summary: 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 \(\mathrm{SL}(3,\mathbb{R})\times\mathrm{SL}(3,\mathbb{R})\) Chern-Simons formulation were found, and were proposed to play the role of black holes. However, in the gauge employed there, the spacetime metric describes a traversable wormhole connecting two asymptotic regions, rather than a black hole. In this paper, we show explicitly that under a higher spin gauge transformation these solutions can be transformed to describe black holes with manifestly smooth event horizons, thereby changing the spacetime causal structure. A related aspect is that the Chern-Simons theory admits two distinct \(\mathrm{AdS}_{3}\) vacua with different asymptotic \(W\)-algebra symmetries and central charges. We show that these vacua are connected by an explicit, Lorentz symmetry-breaking RG flow, of which our solutions represent finite temperature generalizations. These features will be present in any \(\mathrm{SL}(N,\mathbb{R})\times\mathrm{SL}(N,\mathbb{R})\) Chern-Simons theory of higher spins.

MSC:

83C57 Black holes
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C47 Methods of quantum field theory in general relativity and gravitational theory
81T13 Yang-Mills and other gauge theories in quantum field theory
81V17 Gravitational interaction in quantum theory
58J28 Eta-invariants, Chern-Simons invariants
81T20 Quantum field theory on curved space or space-time backgrounds
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
81T17 Renormalization group methods applied to problems in quantum field theory
81R40 Symmetry breaking in quantum theory

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