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arXiv · 2303.16162

T-duality as Correspondences of Categorified Principal Bundles with Adjusted Connections

Hyungrok Kim·Christian Saemann
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Abstract

We provide a pedagogical introduction to the theory of principal 2-bundles with adjusted connections and show how they enter the description of geometric and non-geometric T-dualities as proposed in arXiv:2204.01783. This description combines the torus fibrations as well as the gerbe containing the Kalb-Ramond $B$-field into a single geometric object, a particular case of a non-abelian gerbe. The $B$-field and the metric are encoded in the connection of this categorified principal bundle, and a T-duality is described as a particular span or correspondence of such bundles. The formalism is manifestly covariant under the full T-duality group, and it readily reproduces key examples from the literature.

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Hyungrok Kim, Christian Saemann. 2023-03-28. T-duality as Correspondences of Categorified Principal Bundles with Adjusted Connections. https://arxiv.org/abs/2303.16162

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