Integrability of D1-brane on Group Manifold

TL;DR

This paper investigates the integrability of D1-branes on group manifolds, demonstrating that their equations of motion admit a Lax connection and Poisson brackets similar to principal chiral models, even with non-zero NS-NS flux.

Contribution

It shows that D1-branes on group manifolds are integrable systems, extending known results to backgrounds with non-zero NS-NS two-form.

Findings

D1-brane equations of motion admit a Lax connection

Poisson brackets of Lax connection match principal chiral model structure

Integrability persists with non-zero NS-NS flux

Abstract

This paper is devoted to the analysis of the integrability of D1-brane on group manifold. We consider D1-brane as principal chiral model, determine corresponding equations of motions and find Lax connection. Then we calculate the Poisson brackets of Lax connection and we find that it has similar structure as in case of principal chiral model. As the second example we consider more general background with non-zero NS-NS two form. We again show that D1-brane theory is integrable on this background and determine Poisson brackets of Lax connection.