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

Hyungrok Kim; Christian Saemann

doi:10.22323/1.436.0336

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

Hyungrok Kim, Christian Saemann

Research output: Contribution to journal › Conference article › peer-review

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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.

Original language	English
Article number	336
Journal	Proceedings of Science
Volume	436
DOIs	https://doi.org/10.22323/1.436.0336
Publication status	Published - 8 Nov 2023
Event	Corfu Summer Institute 2022: 22nd Hellenic School and Workshops on Elementary Particle Physics and Gravity - Corfu, Greece Duration: 28 Aug 2022 → 1 Oct 2022

Keywords

hep-th
math-ph
math.MP

ASJC Scopus subject areas

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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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N2 - 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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T-duality as Correspondences of Categorified Principal Bundles with Adjusted Connections

Abstract

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