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The insidious bicategory of algebra bundles

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arxiv 2204.03900 v1 pith:ACP3ZXZ2 submitted 2022-04-08 math.DG math.ATmath.KT

Peter Kristel , Matthias Ludewig , Konrad Waldorf This is my paper · ORCID
classification math.DGmath.ATmath.KT
keywords bundlesbicategoryalgebrabimodulesaddressaddressedalgebrasbeen
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In this paper we construct a bicategory of (super) algebra bundles over a smooth manifold, where the 1-morphisms are bundles of bimodules. The main point is that naive definitions of bimodule bundles will not lead to a well-defined composition law in such a bicategory, at least not if non-invertible bimodules and non-semisimple algebras are desired. This problem has not been addressed so far in the literature. We develop a complete solution, and also address symmetric monoidal structures as well as the corresponding questions of dualizability.

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  1. Categorified structures over moduli spaces: Anomalies, non-invertible symmetries, and exceptional holonomy

    hep-th 2025-06 conditional novelty 7.0 of 10

    The paper conjectures that non-invertible Ising and tricritical Ising symmetries organize closed string states and D-brane categories into categorical bundles over moduli spaces of exceptional holonomy compactifications.

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