Open string T-duality in a weakly curved background

TL;DR

This paper explores T-duality of open strings in a weakly curved background, deriving the T-dual theory by extending the generalized Buscher procedure and analyzing boundary conditions.

Contribution

It extends the generalized Buscher procedure to open strings in weakly curved backgrounds, deriving the open string T-dual from the effective closed string theory.

Findings

Derived the T-dual of open string theory in a weakly curved background.

Showed the transformation of open string boundary conditions to effective closed string theory.

Established a method to obtain open string T-dual via effective theory.

Abstract

We consider a theory of an open string moving in a weakly curved background, composed of a constant metric and a linearly coordinate dependent Kalb-Ramond field with an infinitesimal field strength. We find its T-dual using the generalized Buscher procedure developed for the closed string moving in a weakly curved background, and the fact that solving the boundary conditions, the open string theory transforms to the effective closed string theory. So, T-dualizing the effective theory along all effective directions we obtain its T-dual theory and resume the open sting theory which has such an effective theory. In this way we obtain the open string theory T-dual.