T-duality for principal torus bundles and dimensionally reduced Gysin sequences

TL;DR

This paper explores T-duality for principal torus bundles, extending Gysin sequences, and shows that T-duals with H-flux can be noncommutative, nonassociative tori, revealing complex geometric and algebraic structures.

Contribution

It constructs a Gysin sequence for principal torus bundles and analyzes the nature of T-duals with H-flux, highlighting their noncommutative and nonassociative properties.

Findings

T-duality relates principal torus bundles with H-flux to noncommutative, nonassociative tori.

A Gysin sequence for principal torus bundles is developed.

T-duals with H-flux are generally continuous fields of complex tori.

Abstract

We reexamine the results on the global properties of T-duality for principal circle bundles in the context of a dimensionally reduced Gysin sequence. We will then construct a Gysin sequence for principal torus bundles and examine the consequences. In particular, we will argue that the T-dual of a principal torus bundle with nontrivial H-flux is, in general, a continuous field of noncommutative, nonassociative tori.