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.

Cited by in corpus (4)

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• Arithmetic of Quantum Entropy Function
• Topologically massive gravity on AdS${}_2$ spacetimes
• ZZ boundary states and fragmented AdS2 spaces