2D gravity on AdS 2 with Chern-Simons corrections

Abstract

We study 2D Maxwell-dilaton gravity with higher order corrections given by the Chern-Simons term. The model admits three distinctive AdS 2 vacuum solutions. By making use of the entropy function formalism we find the entropy of the solutions which is corrected due to the presence of the Chern-Simons term. We observe that the form of the correction depends not only on the coefficient of the Chern-Simons term, but also on the sign of the electric charge; pointing toward the chiral nature of the dual CFT. Using the asymptotic symmetry of the theory as well as requiring a consistent picture we can find the central charge and the level of U(1) current. Upon uplifting the solutions to three dimensions we get purely geometric solutions which will be either AdS 3 or warped AdS 3 with an identification.