T-duality diagram for a weakly curved background

TL;DR

This paper extends the T-duality framework to weakly curved backgrounds, constructing a comprehensive diagram that links geometric and non-geometric string theories through all possible T-dualizations.

Contribution

It develops a complete T-dualization diagram for weakly curved backgrounds, revealing the group structure and nonlocality of the resulting theories.

Findings

The T-dualization set forms an Abelian group.

Initial theory is geometric; others are non-geometric and nonlocal.

Complete T-dualization diagram connecting all coordinate choices.

Abstract

In one of our previous papers we generalized the Buscher T-dualization procedure. Here we will investigate the application of this procedure to the theory of a bosonic string moving in the weakly curved background. We obtain the complete T-dualization diagram, connecting the theories which are the result of the T-dualizations over all possible choices of the coordinates. We distinguish three forms of the T-dual theories: the initial theory, the theory obtained T-dualizing some of the coordinates of the initial theory and the theory obtained T-dualizing all of the initial coordinates. While the initial theory is geometric, all the other theories are non geometric and additionally nonlocal. We find the T-dual coordinate transformation laws connecting these theories and show that the set of all T-dualizations forms an Abelian group.