CENTRAL CHARGE FOR AdS2 QUANTUM GRAVITY

Two-dimensional Maxwell-dilaton quantum gravity on AdS2 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 = 3kEl/4 where k is the level of the U(1) current. This is an AdS2 analog of the Brown-Henneaux formula c = 3l/2G for the central charge of quantum gravity on AdS3.