Central charge for AdS 2 quantum gravity

Abstract

Two-dimensional Maxwell-dilaton quantum gravity on AdS 2 with radius ℓ and a constant electric field E is studied. In conformal gauge, this is equivalent to a CFT on a strip. In order to maintain consistent boundary conditions, the usual conformal diffeomorphisms must be accompanied by a certain U(1) gauge transformation. The resulting conformal transformations are generated by a twisted stress tensor, which has a central charge c = 3kE 2ℓ 4/4 where k is the level of the U(1) current. This is an AdS 2 analog of the Brown-Henneaux formula c = 3ℓ/2G for the central charge of quantum gravity on AdS 3. © 2009 SISSA.