Central Charge for \(AdS_2\) Quantum Gravity

Abstract

Two-dimensional Maxwell-dilaton quantum gravity on (AdS_2) with radius (\ell) 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 E^2 \ell^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\ell/2G) for the central charge of quantum gravity on (AdS_3).