Universal non-invertible symmetries

Journal article

It is well-known that gauging a finite 0-form symmetry in a quantum field theory leads to a dual symmetry generated by topological Wilson line defects. These are described by the representations of the 0-form symmetry group which form a 1-category. We argue that for a d-dimensional quantum field theory the full set of dual symmetries one obtains is in fact much larger and is described by a $(d-1)$-category, which is formed out of lower-dimensional topological quantum field theories with the same 0-form symmetry. We study in detail a 2-categorical piece of this $(d-1)$-category described by 2d topological quantum field theories with 0-form symmetry. We further show that the objects of this 2-category are the recently discussed 2d condensation defects constructed from higher-gauging of Wilson lines. Similarly, dual symmetries obtained by gauging any higher-form or higher-group symmetry also form a $(d-1)$-category formed out of lower-dimensional topological quantum field theories with that higher-form or higher-group symmetry. A particularly interesting case is that of the 2-category of dual symmetries associated to gauging of finite 2-group symmetries, as it describes non-invertible symmetries arising from gauging 0-form symmetries that act on $(d-3)$-form symmetries. Such non-invertible symmetries were studied recently in the literature via other methods, and our results not only agree with previous results, but our approach also provides a much simpler way of computing various properties of these non-invertible symmetries. We describe how our results can be applied to compute non-invertible symmetries of various classes of gauge theories with continuous disconnected gauge groups in various spacetime dimensions. We also discuss the 2-category formed by 2d condensation defects in any arbitrary quantum field theory.

Authors: Bhardwaj, L; Schäfer-Nameki, S; Wu, J

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Wiley
• Journal: Fortschritte der Physik
• Volume: 70
• Issue: 11
• Article number: 2200143
• Publication date: 2022-10-05
• Acceptance date: 2022-09-09
• DOI: 10.1002/prop.202200143
• EISSN: 1521-3978
• ISSN: 0015-8208
• Language: English
• Keywords: FFR