Effective Action, Boundary Conditions, and Virasoro Algebra for AdS${}_3$

Abstract

We construct, to second order, the effective action of General Relativity for small excitations generated by a vector field and use it to study conformal symmetry in the boundary of AdS${}_3$. By requiring finiteness of the boundary effective action(s) for certain asymptotic transformations, we derive the well-known Virasoro algebra and central charge associated with the boundary of AdS${}_3$. The bulk action for these transformations can be arbitrarily small.

12 pages, no figures

References in corpus (6)

• The Black Hole in Three Dimensional Space Time
• Geometry of the 2+1 Black Hole
• Black Hole Entropy from Near-Horizon Microstates
• The Kerr/CFT Correspondence
• The Extreme Kerr Throat Geometry: A Vacuum Analog of AdS_2 x S^2
• Hidden Conformal Symmetry of the Kerr Black Hole

Cited by in corpus (7)

• Enhanced asymptotic symmetry algebra of AdS3
• Gravity Waves from Kerr/CFT
• Conformal Chern-Simons holography - lock, stock and barrel
• Hidden Conformal Symmetry of Kerr-Bolt Spacetimes
• Holographic Dual of Linear Dilaton Black Hole in Einstein-Maxwell-Dilaton-Axion Gravity
• Hidden conformal symmetry for Kerr-Newman-NUT-AdS black holes
• Hawking Radiation and Entropy from Horizon Degrees of Freedom