Duality and $O(d,d)$ Symmetries in String Theory

TL;DR

This paper demonstrates that the evolution equations of a closed bosonic string in time-dependent backgrounds are invariant under $O(d,d)$ duality transformations, and the effective actions for original and dual strings are equivalent at tree level.

Contribution

It establishes the $O(d,d)$ invariance of string evolution equations and shows the equivalence of their effective actions under duality transformations.

Findings

$O(d,d)$ invariance of evolution equations

Equivalence of tree level effective actions

Duality transformation on string coordinates

Abstract

The evolution of a closed bosonic string is envisaged in the time-dependent background of its massless modes. A duality transformation is implemented on the spatial component of string coordinates to obtain a dual string. It is shown that the evolution equations are manifestly $O(d,d)$ invariant. The tree level string effective actions for the original and the dual string theory are shown to be equivalent.