Colliding String Waves and Duality

TL;DR

This paper explores the collision of string-theoretic plane waves in higher dimensions, utilizing a coset space reformulation to generate new solutions and connect with integrable systems in two-dimensional gravity.

Contribution

It introduces a coset space approach to analyze string wave collisions, enabling the generation of new backgrounds and linking to classical integrable systems.

Findings

Demonstrated $O(d,d)$ invariance in the effective action

Developed a method to generate new solutions from known backgrounds

Provided explicit examples in four-dimensional spacetime

Abstract

The collision of plane waves corresponding to massless states of closed string is considered in $D$-dimensional space-time. The reduced tree level effective action is known to be manifestly $O(d,d)$ invariant, $d$ being the number of transverse spatial dimensions in the collision process. We adopt a coset space reformulation of the effective two dimensional theory and discuss the relation of this process with classical integrable systems in two dimensions in the presence of gravity. We show how it is possible to generate new backgrounds for the scattering process, from known background solutions to the equations of motion, in the coset reformulation. We present explicit calculations for the case of four space-time dimensions as an illustrative example.