T-duality of a bosonic string in a weakly curved space-time

TL;DR

This paper investigates T-duality of a 3D bosonic string in a weakly curved space-time with coordinate-dependent metric, extending the Buscher procedure to non-isometric backgrounds and analyzing the resulting geometric structure.

Contribution

It generalizes the Buscher T-duality procedure to coordinate-dependent backgrounds lacking translational symmetry, specifically for a weakly curved space-time.

Findings

Derived T-dual transformation laws for coordinate-dependent backgrounds.

Analyzed the geometric structure of the T-dual theory.

Extended T-duality applicability to non-isometric space-times.

Abstract

In this article we consider T-dualization of a $3D$ closed bosonic string that is propagating in space-time metric that has infinitesimal linear dependence on the coordinates $x^\mu$. 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 T-dual theory we will employ generalization of the Buscher procedure that can be applied to such cases where we have coordinate dependent fields that do not possess translational isometry. Finally, using transformation laws that connect coordinates of starting and T-dual theories, we will be able to examine the geometric structure of T-dual theory.