String Theory, Black Holes, and SL(2,R) Current Algebra

TL;DR

This paper explores the $SL(2,R)$ black hole using advanced algebraic techniques, revealing new structures in its string theory description and identifying deformations that affect the spacetime and string modes.

Contribution

It extends Kac-Moody current algebra methods to non-compact groups, uncovering the ground ring, W-infinity structures, and marginal deformations of the black hole.

Findings

Identification of the ground ring elements.

Discovery of W-infinity type structure in fusion algebra.

Deformations that modify spacetime and activate string modes.

Abstract

We analyse in detail the $SL(2,R)$ black hole by extending standard techniques of Kac-Moody current algebra to the non-compact case. We construct the elements of the ground ring and exhibit W-infinity type structure in the fusion algebra of the discrete states. As a consequence, we can identify some of the exactly marginal deformations of the black hole. We show that these deformations alter not only the spacetime metric but also turn on non-trivial backgrounds for the tachyon and all of the massive modes of the string.