Generalized Duality and Singular Strings in Higher Dimensions

TL;DR

This paper constructs and solves deformed gauged WZW models for any pair (G,H), demonstrating dualities, and explores their implications for three-dimensional string theory and Einstein's gravity with new singular solutions.

Contribution

It generalizes duality in gauged WZW models to higher dimensions and explicitly solves classical equations for various (G,H) pairs, including AdS strings.

Findings

Models exhibit duality with identical normal modes.

Explicit solutions for metrics and dilaton fields in 3D string theory.

Discovery of new singular solutions in Einstein's gravity.

Abstract

Deformations of gauged WZW actions are constructed for any pair $(G,H)$ by taking different embeddings of the gauge group $H\subset G$ as it acts on the left and right of the group element $g$. This leads to models that are dual to each other, generalizing the axial/vector duality of the two dimensional black hole manifold. The classical equations are completely solved for any pair $(G,H)$ and in particular for the anti de Sitter string based on $SO(d- 1,2)/SO(d-1,1)$ for which the normal modes are determined. Duality is demonstrated for models that have the same set of normal modes. Concentrating on $SO(2,2)/SO(2,1)$, the metric and dilaton fields of the $d=3$ string as well as some of the dual generalizations are obtained. They have curvature singularities and represent new singular solutions of Einstein's general relativity in three dimensions.