T-duality in the weakly curved background

TL;DR

This paper develops a method for constructing T-dual theories of closed strings in weakly curved backgrounds, resulting in a non-geometric double space framework and demonstrating the reversibility of T-duality transformations.

Contribution

It introduces a procedure for T-duality in weakly curved backgrounds with coordinate-dependent Kalb-Ramond fields, extending T-duality to non-geometric double space.

Findings

Constructed T-dual theory in non-geometric double space.

Demonstrated T-duality transformations are reversible.

Established relations between equations of motion and winding modes.

Abstract

We consider the closed string propagating in the weakly curved background which consists of constant metric and Kalb-Ramond field with infinitesimally small coordinate dependent part. We propose the procedure for constructing the T-dual theory, performing T-duality transformations along coordinates on which the Kalb-Ramond field depends. The obtained theory is defined in the non-geometric double space, described by the Lagrange multiplier $y_\mu$ and its $T$-dual $\tilde{y}_\mu$. We apply the proposed T-duality procedure to the T-dual theory and obtain the initial one. We discuss the standard relations between T-dual theories that the equations of motion and momenta modes of one theory are the Bianchi identities and the winding modes of the other.