(Super-) String in Two Dimensional Black Hole and Target Space Dualities

TL;DR

This paper reviews string theory in two-dimensional black hole backgrounds, focusing on target space dualities, their explicit formulas, and the extension to superstring theory using supersymmetric models.

Contribution

It introduces a general formula connecting dual target space manifolds with Killing symmetries and discusses superstring theory in this context.

Findings

Duality in target space resembles R→1/R symmetry.

Explicit formula connecting dual manifolds with Killing symmetries.

Extension to superstring theory via supersymmetric gauged Wess-Zumino-Witten model.

Abstract

We review the recently proposed string theory in two dimensional black hole background. Especially, the structure of the duality in the target space is discussed. The duality is analogous to \lq\lq $R \rightarrow 1/R$" symmetry of a compactified boson. We consider the duality in more general target space manifolds which have Killing symmetries and we give an explicit formula which connects two different manifolds which are dual to each other. Superstring theory in two dimensional black hole background is also discussed based on supersymmetric $SU(1,1)/U(1)$ gauged Wess-Zumino-Witten model.