Chemical potentials in three-dimensional higher spin anti-de Sitter gravity

Abstract

We indicate how to introduce chemical potentials for higher spin charges in higher spin anti-de Sitter gravity in a manner that manifestly preserves the original asymptotic W-symmetry. This is done by switching on a non-vanishing component of the connection along the temporal (thermal) circles. We first recall the procedure in the pure gravity case (no higher spin) where the only "chemical potentials" are the temperature and the chemical potential associated with the angular momentum. We then generalize to the higher spin case. We find that there is no tension with the W(N) or W(infinity) asymptotic algebra, which is obviously unchanged by the introduction of the chemical potentials. Our argument is non-perturbative.

Minor misprints corrected

References in corpus (7)

• 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
• Symmetries of Holographic Minimal Models
• Generalized Black Holes in Three-dimensional Spacetime
• Quantum W-symmetry in AdS_3
• W Symmetry and Integrability of Higher spin black holes
• Observables and Microscopic Entropy of Higher Spin Black Holes

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