SciPost Submission Page
Monopole Breaking of Chern-Weil Symmetries
by Eduardo García-Valdecasas, Matthew Reece, Motoo Suzuki
Submission summary
| Authors (as registered SciPost users): | Eduardo Garcia Valdecasas · Matthew Reece |
| Submission information | |
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| Preprint Link: | scipost_202410_00015v1 (pdf) |
| Date submitted: | 2024-10-09 18:31 |
| Submitted by: | Garcia Valdecasas, Eduardo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Gauge theories in $d$ dimensions with a nontrivial fundamental group admit a $(d-3)$-form magnetic symmetry and a $(d-5)$-form instantonic symmetry. These are examples of Chern-Weil symmetries, with conserved currents built out of the gauge field strength, which can only be explicitly broken through violations of the Bianchi identity. For U(1) gauge theory, it is clear that magnetic monopoles violate not only the $(d-3)$-form magnetic symmetry but also lower-form symmetries like the instantonic symmetry. It is also known that an improved instanton number symmetry current, which is conserved, can be constructed in the case that the magnetic monopole admits a dyonic excitation. We study the generalization to other gauge groups, showing that magnetic monopoles also violate instantonic symmetries for nonabelian groups like PSU($n$), and that dyon modes can restore such symmetries. Furthermore, we show that in many (but not all) examples where a gauge group $G$ is Higgsed to a gauge group $H$, the structure of monopoles and dyons emerging from the Higgsing process explicitly breaks the instantonic symmetries of $H$ to those of $G$. The meaning of explicit breaking of a $(d-5)$-form symmetry is clearest for $d > 4$, but these results also extend to $d = 4$, where the breaking is interpreted as an obstruction to coupling the theory to a background axion field.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Report
In this manuscript, the authors explore the connection between the explicit breaking of $(d-3)$-form magnetic symmetries and the breaking of $(d-5)$-form instantonic symmetries. This builds on an intriguing strain of the authors' earlier work, including from the perspective of the effects of loops of magnetic monopoles, which had been crying out for further understanding. Various works utilizing generalized symmetries in particle physics have implicitly relied on this connection, but concrete understanding thereof had been absent from the literature. It is the $d=4$ case which is of course most useful for real-world physics, but this is also the most subtle case where the instantonic symmetry must be interpreted as a subtle sort of `$(-1)$-form symmetry', so this general study putting $d=4$ on roughly even footing with the higher-dimensional case is particularly valuable.
This is a great paper doing important field theory which needs to be understood in order to clearly see the impact of generalized symmetries on phenomenology. The investigation is thorough and contains useful explicit detail and calculation. The authors have put clear effort into providing pedagogical explanations of their investigation and results. The 2d toy models introduced in Section 2 are especially valuable as a simple setting in which the reader can get a handle on what is happening before having to discuss gauge theories. More-complicated scenarios are built up slowly, and the interesting features of each example are picked apart with lessons to be learned highlighted.
This work at the interface of formal and phenomenological field theory is a big, concrete step toward a full understanding of the breaking of Chern-Weil symmetries which will allow clearer use of these ideas in particle physics.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)