A note on covariant action integrals in three dimensions

Abstract

We compute -in the saddle point approximation- the partition function for the 2+1 black hole using the Gibbons-Hawking approach. Some issues concerning the definition of thermodynamical ensembles are clarified. It is pointed out that the right action in covariant form is exactly equal to the Chern-Simons action with no added boundary terms. This action is finite, yields the right canonical free energy and has an extremum when the temperature and angular velocity are fixed. The correspondence with a 1+1 $CFT$ is indicated.

Some improvments in the text and references added. 5 pages (two column), Latex, no figures

References in corpus (5)

• Gauge Theory Correlators from Non-Critical String Theory
• The Holographic Weyl anomaly
• Black Hole Entropy from Near-Horizon Microstates
• Boundary dynamics and the statistical mechanics of the 2+1 dimensional black hole
• Anti-de Sitter/CFT Correspondence in Three-Dimensional Supergravity

Cited by in corpus (25)

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• On boundary conditions in three-dimensional AdS gravity
• Asymptotic symmetries of three-dimensional Chern-Simons gravity for the Maxwell algebra
• A Neumann Boundary Term for Gravity
• Holonomies, anomalies and the Fefferman-Graham ambiguity in AdS3 gravity
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity I - Convergence of multiple approaches and examples of Ponzano-Regge statistical duals
• Kac-Moody and Virasoro Characters from the Perturbative Chern-Simons Path Integral
• Holography in 3D AdS gravity with torsion
• Thermodynamics and Statistical Mechanics of Induced Liouville Gravity
• A Dynamical Boundary for Anti-de Sitter Space
• Testing Holographic Principle from Logarithmic and Higher Order Corrections to Black Hole Entropy
• How to make the gravitational action on non-compact space finite
• Covariant description of the black hole entropy in 3D gravity
• Three-dimensional black hole entropy
• Covariant Differential Identities and Conservation Laws in Metric-Torsion Theories of Gravitation. II. Manifestly Generally Covariant Theories
• Twisted sectors in three-dimensional gravity
• Vacuum energy in asymptotically flat 2+1 gravity
• Pure and Twisted Holography
• The covariant action of higher spin black holes in three dimensions
• Holographic Renormalization of 3D Minimal Massive Gravity
• On Modular Invariance and 3D Gravitational Instantons
• Asymptotic Chern-Simons formulation of spacelike stretched AdS gravity
• Aspects of Higher Spin Theories, Conformal Field Theories and Holography