2023/03/28 by Hyungrok Kim, Kim, Hyungrok, Christian Saemann +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Microtubule and mitosis dynamics
paper · pdf · doi:10.48550/arxiv.2303.16162
openalex publication_date 2023/03/28 · openalex created_date 2023/03/31 · openalex updated_date 2026/07/28
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.