Comments on String Theory on $AdS_3$

TL;DR

This paper rigorously derives the spacetime conformal field theory and algebraic structures for string propagation on $AdS_3$, confirming the $AdS$/CFT correspondence in this setting and exploring implications for black hole entropy.

Contribution

It provides a detailed worldsheet analysis of string theory on $AdS_3$, establishing the full $AdS$/CFT correspondence and its relevance to black hole physics.

Findings

Derived the spacetime CFT and algebraic structures for $AdS_3$ string theory

Confirmed the $AdS$/CFT correspondence in this context

Discussed implications for BTZ black holes and entropy

Abstract

We study string propagation on $AdS_3$ times a compact space from an ``old fashioned'' worldsheet point of view of perturbative string theory. We derive the spacetime CFT and its Virasoro and current algebras, thus establishing the conjectured $AdS$/CFT correspondence for this case in the full string theory. Our results have implications for the extreme IR limit of the $D1-D5$ system, as well as to 2+1 dimensional BTZ black holes and their Bekenstein-Hawking entropy.