T-dualization in a curved background in absence of a global symmetry

TL;DR

This paper extends T-duality analysis to weakly curved backgrounds with coordinate-dependent metrics lacking global symmetry, redefining the Buscher procedure for broader applicability in string theory.

Contribution

It introduces a modified T-dualization method applicable to backgrounds without global shift symmetry, specifically for second-order weakly curved geometries.

Findings

Redefinition of T-dualization procedure for non-symmetric backgrounds

Application to second-order weakly curved backgrounds with nonzero Ricci tensor

Demonstration of T-duality in absence of global symmetry

Abstract

We investigate T-duality of a closed string moving in a weakly curved background of the second order. A previously discussed weakly curved background consisted of a flat metric and a linearly coordinate dependent Kalb-Ramond field with an infinitesimal strength. The background here considered differs from the above in a coordinate dependent metric of the second order. Consequently, the corresponding Ricci tensor is nonzero. As this background does not posses the global shift symmetry the generalized Buscher T-dualization procedure is not applicable to it. We redefine it and make it applicable to backgrounds without the global symmetry.