Integrability of D1-brane on Group Manifold with Mixed Three Form Flux

TL;DR

This paper investigates the integrability of a D1-brane on a group manifold with mixed three-form fluxes by constructing a Lax connection and analyzing its Poisson brackets.

Contribution

It provides the explicit form of the Lax connection and demonstrates the integrability of the D1-brane system with mixed fluxes.

Findings

Lax connection constructed for the D1-brane system

Poisson brackets calculated confirming integrability

Theoretical framework established for further studies

Abstract

We consider D1-brane as a natural probe of the group manifold with mixed three form fluxes. We determine Lax connection for given theory. Then we switch to the canonical analysis and calculate the Poisson brackets between spatial components of Lax connections and we argue for integrability of given theory.