Central Charge for AdS_2 Quantum Gravity

Two-dimensional Maxwell-dilaton quantum gravity on AdS_2 with radius 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=3k E² ⁴/4 where k is the level of the U(1) current. This is an AdS_2 analog of the Brown-Henneaux formula c = 3/2G for the central charge of quantum gravity on AdS_3.