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On anomalies and gauging of U(1) non-invertible symmetries in 4d QED
by Avner Karasik
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Submission summary
| Authors (as registered SciPost users): | Avner Karasik |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2211.05802v3 (pdf) |
| Date accepted: | 2023-04-13 |
| Date submitted: | 2023-03-09 12:04 |
| Submitted by: | Karasik, Avner |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In this work we propose a way to promote the anomalous axial U(1) transformations to exact non-invertible U(1) symmetries. We discuss the procedure of coupling the non-invertible symmetry to a (dynamical or background) gauge field. We show that as part of the gauging procedure, certain constraints are imposed to make the gauging consistent. The constraints emerge naturally from the form of the non-invertible U(1) conserved current. In the case of dynamical gauging, this results in new type of gauge theories we call non-invertible gauge theories: These are gauge theories with additional constraints that cancel the would-be gauge anomalies. By coupling to background gauge fields, we can discuss 't-Hooft anomalies of non-invertible symmetries. We show in an example that the matching conditions hold but they are realized in an unconventional way. Turning on non-trivial background for the non-invertible gauge field changes the vacuum even when the symmetry is not broken and the background is very weak. The anomalies are then matched by the appearance of solitons in the new vacuum.
List of changes
1) Added an appendix to explain a subtle factor of 2 computation.
2) page 7: Explained in detail why the operator in (2.6) is indeed topological.
3) Page 9: Showed that for every rational angle, the previous constructions coincide with the one presented in the paper.
4) Corrected the description of anomalies after (1.1).
5) page 7: deleted the word "discrete" when talking about the group of rational numbers.
6) Deleted the comment about the defects VS operators and their normalization
Published as SciPost Phys. 15, 002 (2023)
Anonymous on 2023-03-14 [id 3481]
The revised version addresses all the previous comments, and I recommend its publication in SciPost.