Exact Duality and Nilpotent Gauging

TL;DR

This paper introduces a new duality transformation called nilpotent duality, linking exact string backgrounds such as the $SL(2, R)$ WZW model and plane wave geometries, expanding the understanding of string dualities.

Contribution

It defines nilpotent duality transformations and demonstrates their application to relate the $SL(2, R)$ WZW model with three-dimensional plane wave geometries.

Findings

The $SL(2, R)$ WZW model transforms into a plane wave geometry via nilpotent duality.

An inverse transformation from plane wave to $SL(2, R)$ model is established.

Implications for string theory dualities are discussed.

Abstract

We obtain new duality transformations relating some exact string backgrounds, by defining the nilpotent duality. We show that the ungauged $SL(2, R)$ WZW model transforms by its action into the three dimensional plane wave geometry. We also give the inverse transformation from the plane wave to the $SL(2, R)$ model and discuss the implications of the results.