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

TL;DR

This work generalizes topological spherical T-duality to oriented $S^{2n-1}$-bundles equipped with closed odd fluxes of arbitrary degree, establishing the existence of T-duals when the fiber-integrated flux is integral and proving isomorphisms of twisted cohomology between dual spaces. It develops a higher geometric framework by introducing an extended (higher) Courant algebroid $C_\psi$ on the base and shows that spherical T-duality induces an isomorphism $\mathcal{T}_F$ between extended Courant algebroids, thereby realizing geometric spherical duality. A corresponding Fourier–Mukai-type interpretation yields isomorphisms of twisted K-theories for unimodular dual pairs, linking cohomological and K-theoretic aspects of the duality. The paper also provides concrete examples and outlines an extensive outlook on connections to exceptional generalized geometry and potential physical implications of dimension-changing dualities.

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.

Theorems & Definitions (45)

• Definition 2.1
• Lemma 2.2
• proof
• Lemma 2.3
• proof
• Lemma 2.4
• proof
• Definition 3.1
• Lemma 3.2: Bott--Tu bott-tu, pg 118-119
• Definition 3.3