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Gauging Noninvertible Defects: A 2-Categorical Perspective

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arxiv 2211.08436 v2 pith:W3GZXK2J submitted 2022-11-15 math.CT hep-thmath-phmath.MPmath.QA

Thibault D. Décoppet , Matthew Yu This is my paper · ORCID
classification math.CThep-thmath-phmath.MPmath.QA
keywords categorycondensingnoninvertiblesymmetryadditionalalgebraanomalycategorical
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We generalize the notion of an anomaly for a symmetry to a noninvertible symmetry enacted by surface operators using the framework of condensation in 2-categories. Given a multifusion 2-category, potentially with some additional levels of monoidality, we prove theorems about the structure of the 2-category obtained by condensing a suitable algebra object. We give examples where the resulting category displays grouplike fusion rules and through a cohomology computation, find the obstruction to condensing further to the vacuum theory.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On \'Etale Algebras and Bosonic Fusion 2-Categories

    math.CT 2024-11 conditional novelty 7.0 of 10

    Connected and Lagrangian étale algebras in Z_1(2Vect^π_G) are classified by subgroups, braided fusion categories with group actions, and 4-group morphism data; this yields a parametrization of bosonic fusion 2-categories.

  2. On the Physics of Higher Condensation Defects

    hep-th 2025-06 conditional novelty 6.0 of 10

    Topological defects from higher gauging are shown, via explicit Lagrangian computations, to satisfy the Karoubi completeness condition of Johnson-Freyd's higher fusion categories, and this is identified with splitting...

  3. Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories

    cond-mat.str-el 2024-12 conditional novelty 6.0 of 10

    Non-invertible symmetries in finite-group gauge theories are realized as condensation defects, with a complete Z_N dictionary and new automorphism symmetry expressions.

  4. The Higher Structure of Symmetries of Axion-Maxwell Theory

    hep-th 2024-11 conditional novelty 6.0 of 10

    The paper determines the fusion interfaces and F-symbols for the non-invertible electric 1-form symmetry of 4d axion-Maxwell theory.

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