T-duality for open strings with respect to non-abelian isometries

TL;DR

This paper explores how T-duality transforms boundary conditions in open string sigma models with non-abelian symmetries, revealing the interchange of Neumann and Dirichlet conditions through gauging and integrating out gauge fields.

Contribution

It introduces a method to gauge non-abelian isometries in open string models with boundaries and demonstrates how T-duality affects boundary conditions.

Findings

T-duality interchanges Neumann and Dirichlet boundary conditions.

Gauging non-abelian isometries with boundary conditions is consistent when field strength vanishes.

Integrating out gauge fields yields the T-dual model with transformed boundary conditions.

Abstract

We gauge the non-abelian isometries of a sigma model with boundaries. Forcing the field strength of the gauge fields to vanish renders the gauged model equivalent to the ungauged one provided that boundary conditions are taken into account properly. Integrating out the gauge fields gives the T-dual model. We observe that T-duality interchanges Neumann (or mixed) boundary conditions with Dirichlet boundary conditions.