Higher spin extension of cosmological spacetimes in 3D: asymptotically flat behaviour with chemical potentials and thermodynamics

Abstract

A generalized set of asymptotic conditions for higher spin gravity without cosmological constant in three spacetime dimensions is constructed. They include the most general temporal components of the gauge fields that manifestly preserve the original asymptotic higher spin extension of the BMS${}_3$ algebra, with the same central charge. By virtue of a suitable permissible gauge choice, it is shown that this set can be directly recovered as a limit of the boundary conditions that have been recently constructed in the case of negative cosmological constant, whose asymptotic symmetries are spanned by two copies of the centrally-extended W${}_3$ algebra. Since the generalized asymptotic conditions allow to incorporate chemical potentials conjugated to the higher spin charges, a higher spin extension of locally flat cosmological spacetimes becomes naturally included within the set. It is shown that their thermodynamic properties can be successfully obtained exclusively in terms of gauge fields and the topology of the Euclidean manifold, which is shown to be the one of a solid torus, but with reversed orientation as compared with one of the black holes. It is also worth highlighting that regularity of the fields can be ensured through a procedure that does not require an explicit matrix representation of the entire gauge group. In few words, we show that the temporal components of generalized dreibeins can be consistently gauged away, which partially fixes the chemical potentials, so that the remaining conditions can just be obtained by requiring the holonomy of the generalized spin connection along a thermal circle to be trivial. The extension of the generalized asymptotically flat behaviour to the case of spins $s\ge 2$ is also discussed.

33 pages, one figure. Talk given at the "Meeting on the horizon", Valparaiso, Chile, March 2014

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• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Entropy of three-dimensional asymptotically flat cosmological solutions
• Generalized Black Holes in Three-dimensional Spacetime
• Quantum W-symmetry in AdS_3
• Asymptotic symmetries and dynamics of three-dimensional flat supergravity
• Partition function of free conformal higher spin theory
• Flat space (higher spin) gravity with chemical potentials
• Flat Space Limit of (Higher-Spin) Cardy Formula
• Boundary dynamics of asymptotically flat 3D gravity coupled to higher spin fields
• Unitarity in three-dimensional flat space higher spin theories
• Low Tension Strings on a Cosmological Singularity
• Unitary W-algebras and three-dimensional higher spin gravities with spin one symmetry

Cited by in corpus (6)

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• Higher Spin Black Holes with Soft Hair
• Characters of the BMS Group in Three Dimensions
• Asymptotic structure of $\mathcal{N}=2$ supergravity in 3D: extended super-BMS${}_3$ and nonlinear energy bounds
• Three-dimensional Spin-3 Theories Based on General Kinematical Algebras
• Electrically charged black hole on AdS${}_3$: scale invariance and the Smarr formula