Topological Spherical T-duality -- Dimension change from higher degree $H$-flux

TL;DR

This paper generalizes topological spherical T-duality to sphere bundles with closed odd forms of arbitrary degree, establishing the existence of T-duals and their properties, including isomorphic twisted cohomology and compatible Courant algebroids.

Contribution

It extends the concept of spherical T-duality to higher-degree forms and arbitrary sphere bundle dimensions, broadening the scope of the duality framework.

Findings

T-duals exist for generalized sphere bundles with odd-degree forms.

T-dual spaces have isomorphic twisted cohomology.

Introduces Courant algebroids compatible with spherical T-duality.

Abstract

Topological Spherical T-duality was introduced by Bouwknegt, Evslin and Mathai in [BEM15] as an extension of topological T-duality from $S^1$-bundles to $\mathrm{SU}(2)$-bundles endowed with closed 7-forms. This notion was further extended to sphere bundles by Lind, Sati and Westerland [LSW16] as a duality between $S^{2n-1}$-bundles endowed with closed $(4n-1)$-forms. We generalise this relation one step further and define T-duality for $S^{2n-1}$-bundles endowed with closed odd forms of arbitrary degree. The degree of the form determines the dimension of the fibers of the dual spaces. We show that $T$-duals exist and, as in the previous cases, $T$-dual spaces have isomorphic twisted cohomology. We finish by introducing a version of Courant algebroids which is compatible with spherical T-duality.