Monodromy, Duality 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 the solvable Nappi-Witten model.

Contribution

It introduces a method to construct the monodromy matrix for 2D string actions and explores its transformation under T-duality, with explicit examples.

Findings

Monodromy matrix constructed for 2D string effective action

Pole structure derived from factorizability property

Explicit construction for Nappi-Witten model

Abstract

In this talk, we show how the monodromy matrix, ${\hat{\cal M}}$, can be constructed for the two dimensional tree level string effective action. The pole structure of ${\hat{\cal M}}$ is derived using its factorizability property. It is shown 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.