Central Charge for AdS_2 Quantum Gravity

TL;DR

This paper derives a formula for the central charge in AdS_2 quantum gravity with a Maxwell-dilaton setup, revealing a twisted stress tensor structure influenced by boundary conditions and gauge transformations.

Contribution

It introduces a novel expression for the central charge in AdS_2 gravity, linking it to the electric field, level of the U(1) current, and AdS radius, extending the Brown-Henneaux result.

Findings

Central charge formula: c = (3k E^2 ℓ^4)/4

Twisted stress tensor arises from boundary conditions and gauge transformations

Analog of Brown-Henneaux formula for AdS_2 geometry

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.