O(2,2) Transformations and the String Geroch Group

TL;DR

This paper demonstrates the integrability of certain string background equations with symmetries, revealing an infinite Geroch group that generalizes known dualities and enables solution generation.

Contribution

It introduces the string Geroch group as an infinite symmetry extending $O(2,2)$ and S-duality, providing a new framework for generating and understanding string backgrounds.

Findings

The background equations are integrable with two symmetries.

The string Geroch group generalizes $O(2,2)$ and S-duality.

An additional $Z_2$ symmetry is identified.

Abstract

The 1--loop string background equations with axion and dilaton fields are shown to be integrable in four dimensions in the presence of two commuting Killing symmetries and $\delta c = 0$. Then, in analogy with reduced gravity, there is an infinite group that acts on the space of solutions and generates non--trivial string backgrounds from flat space. The usual $O(2,2)$ and $S$--duality transformations are just special cases of the string Geroch group, which is infinitesimally identified with the $O(2,2)$ current algebra. We also find an additional $Z_{2}$ symmetry interchanging the field content of the dimensionally reduced string equations. The method for constructing multi--soliton solutions on a given string background is briefly discussed.