Duality, Monodromy and Integrability of Two Dimensional String Effective Action

TL;DR

This paper constructs and analyzes the monodromy matrix for two-dimensional string effective actions, revealing its transformation properties under T-duality and applying it to specific models like the Nappi-Witten background and heterotic black holes.

Contribution

It introduces a method to construct the monodromy matrix for complex backgrounds using T-duality and explicitly computes it for notable models, enhancing understanding of integrability in string theory.

Findings

Monodromy matrix transforms non-trivially under T-duality.

Explicit construction of monodromy matrix for Nappi-Witten model.

Monodromy matrix for Schwarzschild black hole in heterotic string theory.

Abstract

The monodromy matrix, ${\hat{\cal M}}$, is constructed for two dimensional tree level string effective action. The pole structure of ${\hat{\cal M}}$ is derived using its factorizability property. It is found that the monodromy matrix transforms non-trivially under the non-compact T-duality group, which leaves the effective action invariant and this can be used to construct the monodromy matrix for more complicated backgrounds starting from simpler ones. We construct, explicitly, ${\hat{\cal M}}$ for the exactly solvable Nappi-Witten model, both when B=0 and $B\neq 0$, where these ideas can be directly checked. We consider well known charged black hole solutions in the heterotic string theory which can be generated by T-duality transformations from a spherically symmetric `seed' Schwarzschild solution. We construct the monodromy matrix for the Schwarzschild black hole background of the heterotic string theory.