Open string T-duality in a weakly curved background

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 string theory which has such an effective theory. In this way we obtain the open string theory T-dual.