# Central Charge for $$AdS_2$$ Quantum Gravity

 Title: Central Charge for $$AdS_2$$ Quantum Gravity Author: Hartman, Thomas; Strominger, Andrew E. Note: Order does not necessarily reflect citation order of authors. Citation: Hartman, Thomas, and Andrew E. Strominger. 2009. Central charge for $$AdS_2$$ quantum gravity. Journal of High Energy Physics 2009(4): 26. Full Text & Related Files: 0803.3621v1.pdf (122.5Kb; PDF) 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 $$AdS_3$$. Published Version: doi:10.1088/1126-6708/2009/04/026 Other Sources: http://arxiv.org/abs/0803.3621 Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:8156514 Downloads of this work: