T-Duality of a Bosonic String in a Weakly Curved Space-Time

In this article, the T-dualization of a 3D closed bosonic string, that is propagating in space-time metric with an infinitesimal linear dependence on the coordinates x^μ, is considered. Other fields, Kalb-Ramond and dilaton fields are set to zero. Action with this configuration of fields is not invariant to translations. In order to find the T-dual theory, a generalization of the Buscher procedure is employed, that can be applied to cases with coordinate dependent fields that do not possess translational isometry. Finally, by using transformation laws that connect coordinates of starting and T-dual theories, authors will be able to examine the geometric structure of T-dual theory.