T-duality on Almost Hermitian Spaces

TL;DR

This paper explores how T-duality affects almost bi-hermitian spaces with torsion, revealing conditions under which integrability is preserved or broken, with implications for string compactifications.

Contribution

It provides a complete description of T-duality transformations on geometrical objects and analyzes integrability preservation under T-duality in almost Hermitian spaces.

Findings

Hermiticity alone does not ensure integrability after T-duality.

Kähler condition preserves integrability under T-duality.

H-flux form is suitable for string compactification scenarios.

Abstract

We investigate T-duality transformation on an almost bi-hermitian space with torsion. By virtue of the Buscher rule, we completely describe not only the covariant derivative of geometrical objects but also the Nijenhuis tensor. We apply this description to an almost bi-hermitian space with isometry and investigate integrability on its T-dualized one. We find that hermiticity is not a sufficient condition to preserve integrability under T-duality transformations. However, in the presence of the K\"{a}hler condition, the T-dualized space still admits integrability of the almost complex structures. We also observe that the form of H-flux is suitable for string compactification scenarios.