Two Dimensional Anti-de Sitter Space and Discrete Light Cone Quantization

Abstract

We realize the two dimensional anti-de Sitter ($AdS_2$) space as a Kaluza-Klein reduction of the $AdS_3$ space in the framework of the discrete light cone quantization (DLCQ). Introducing DLCQ coordinates which interpolate the original (unboosted) coordinates and the light cone coordinates, we discuss that $AdS_2/CFT$ correspondence can be deduced from the $AdS_3/CFT$. In particular, we elaborate on the deformation of WZW model to obtain the boundary theory for the $AdS_2$ black hole. This enables us to derive the entropy of the $AdS_2$ black hole from that of the $AdS_3$ black hole.