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arXiv · 2503.20143

T-duality for transgressive fibrations

Gil R. Cavalcanti
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Abstract

We extend the notion of topological T-duality from oriented sphere bundles to transgressive fibrations, a more general type fibration characterised by the abundance of transgressive elements. Examples of transgressive fibrations include principal $\mathrm{U}(n)$-bundles therefore our notion of T-duality belongs to the realm of non-Abelian T-duality. We prove that transgressive T-duals have isomorphic twisted cohomology. We then introduce Clifford--Courant algebroids, show that one can assign such an algebroid to a transgressive fibration and that transgressive T-duals have isomorphic Clifford--Courant algebroids. We provide several examples illustrating different properties of T-dual spaces. A few typos corrected in v2.

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Gil R. Cavalcanti. 2025-03-26. T-duality for transgressive fibrations. https://arxiv.org/abs/2503.20143

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