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

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

2010-07-07

arxiv.org/abs/1007.1031v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, no figures

Scientific paper

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.

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