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

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