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

TL;DR

This paper constructs a two-dimensional anti-de Sitter space via Kaluza-Klein reduction from three dimensions within the discrete light cone quantization framework, and explores its holographic correspondence and black hole entropy.

Contribution

It demonstrates a novel realization of $AdS_2$ space from $AdS_3$ using DLCQ and derives the $AdS_2$ black hole entropy from $AdS_3$ black hole entropy.

Findings

Realization of $AdS_2$ as a Kaluza-Klein reduction of $AdS_3$

Derivation of $AdS_2/CFT$ correspondence from $AdS_3/CFT$

Calculation of $AdS_2$ black hole entropy from $AdS_3$ black hole entropy

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.