Integrability and Generalized Monodromy Matrix

TL;DR

This paper constructs the generalized monodromy matrix for two-dimensional string effective actions, explores integrability conditions, and applies the framework to the exactly solvable WZNW model in a specific limit.

Contribution

It introduces a new construction of the generalized monodromy matrix incorporating T-duality properties and analyzes integrability for specific models.

Findings

Derived integrability conditions with spectral parameter dependence.

Constructed the monodromy matrix for the WZNW model in pp-wave limit.

Demonstrated the applicability of the framework to exactly solvable models.

Abstract

We construct the Generalized Monodromy matrix $\mathcal{\hat{M}}(\omega)$ of two dimensional string effective action by introducing the T-duality group properties.The integrability conditions with general solutions depending on spectral parameter are given. This construction is investigated for the exactly solvable Wess, Zumino, Novikov and Witten (WZNW) model in pp-wave Limit when B=0.