2-d Gravity as a Limit of the SL(2,R) Black Hole

TL;DR

This paper explores how the $SL(2,R)/U(1)$ black hole transforms under a boost, revealing its connection to 2D gravity and showing that its states correspond to those in 2D gravity coupled to matter.

Contribution

It demonstrates that boosting the black hole maps its vertex and discrete states to those of 2D gravity, establishing a link between black hole models and 2D gravitational theories.

Findings

Black hole tachyon operators become those of 2D gravity

Discrete states of black hole match 2D gravity states after boost

Discussion on the fate of extra discrete states

Abstract

The transformation of the $SL(2,R)/U(1)$ black hole under a boost of the subgroup U(1) is studied. It is found that the tachyon vertex operators of the black hole go into those of the $c=1$ conformal field theory coupled to gravity. The discrete states of the black hole also tend to the discrete states of the 2-d gravity theory. The fate of the extra discrete states of the black hole under boost are discussed.