Strings on Curved Spacetimes: Black Holes, Torsion, and Duality

TL;DR

This paper explores string propagation on noncompact coset spaces using gauged WZW models, revealing dualities between black hole and black string geometries with torsion, and classifying models with a single timelike coordinate.

Contribution

It introduces a classification of string models on coset spaces with a single timelike coordinate and analyzes dualities between black hole and black string geometries with torsion.

Findings

Duality maps black hole singularities to regular surfaces in black string geometries.

Explicit classification of models with D ≤ 10 dimensions.

Identification of coset models leading to cosmological string solutions.

Abstract

We present a general discussion of strings propagating on noncompact coset spaces $G/H$ in terms of gauged WZW models, emphasizing the role played by isometries in the existence of target space duality. Fixed points of the gauged transformations induce metric singularities and, in the case of abelian subgroups $H$, become horizons in a dual geometry. We also give a classification of models with a single timelike coordinate together with an explicit list for dimensions $D\leq 10$. We study in detail the class of models described by the cosets $SL(2,\IR)\otimes SO(1,1)^{D-2}/SO(1,1)$. For $D\geq 2$ each coset represents two different spacetime geometries: (2D black hole)$\otimes \IR^{D-2}$ and (3D black string)$\otimes \IR^{D-3}$ with nonvanishing torsion. They are shown to be dual in such a way that the singularity of the former geometry (which is not due to a fixed point) is mapped to a regular surface (i.e.\ not even a horizon) in the latter . These cosets also lead to the conformal field theory description of known and new cosmological string models.