Ehlers Transformations and String Effective Action

TL;DR

This paper generalizes the Ehlers transformation within string theory, demonstrating how twist potentials and moduli fields transform under an $O(d,d)$ symmetry in the effective two-dimensional theory.

Contribution

It explicitly extends the Ehlers transformation to string theory, revealing the $O(d,d)$ symmetry acting on moduli and twist potentials in the effective action.

Findings

Ehlers transformation generalized to string theory.

Twist potential and moduli transform under $O(d,d)$ symmetry.

The $O(d,d)$ action is explicitly characterized.

Abstract

We explicitly obtain the generalization of the Ehlers transformation for stationary axisymmetric Einstein equations to string theory. This is accomplished by finding the twist potential corresponding to the moduli fields in the effective two dimensional theory. Twist potential and symmetric moduli are shown to transform under an $O(d,d)$ which is a manifest symmetry of the equations of motion. The non-trivial action of this $O(d,d)$ is given by the Ehlers transformation and belongs to the set $O(d) \times O(d)\over O(d) $.