Hartman, ThomasStrominger, Andrew2012-02-102009Hartman, Thomas, and Andrew E. Strominger. 2009. Central charge for \(AdS_2\) quantum gravity. Journal of High Energy Physics 2009(4): 26.1029-8479http://nrs.harvard.edu/urn-3:HUL.InstRepos:8156514Two-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 \(AdS_3\).en-UShigh energy physics theoryAdS-CFT correspondence2D gravityspace-time symmetriesdS-CFT correspondencegravitationcosmologyparticle physicsfield theoryJournal Article2012-02-1010.1088/1126-6708/2009/04/026