Duality and Integrability of Two Dimensional String Effective Action

TL;DR

This paper develops a method to construct the monodromy matrix for two-dimensional string effective actions with $O(d,d)$ symmetry, enabling the generation of new solutions via $T$-duality and applying it to the Nappi-Witten model.

Contribution

It introduces a prescription for constructing the monodromy matrix and analyzing its transformation under $T$-duality, extending solution-generating techniques in string theory.

Findings

Constructed the monodromy matrix for $O(d,d)$ invariant actions.

Derived the transformation properties of the monodromy matrix under $T$-duality.

Applied the method to the Nappi-Witten model with and without B-field.

Abstract

We present a prescription for constructing the monodromy matrix, $\hat{\cal M}(\omega)$, for $O(d,d)$ invariant string effective actions and derive its transformation properties under the $T$-duality group. This allows us to construct $\hat{\cal M}(\omega)$ for new backgrounds, starting from known ones, which are related by $T$-duality. As an application, we derive the monodromy matrix for the exactly solvable Nappi-Witten model, both when B=0 and $B\neq 0$.