SciPost Submission Page
Non-invertible symmetries in finite group gauge theory
by Clay Cordova, Davi Bastos Costa, Po-Shen Hsin
Submission summary
| Authors (as registered SciPost users): | Davi Bastos Costa · Po-Shen Hsin |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2407.07964v2 (pdf) |
| Date accepted: | 2024-10-28 |
| Date submitted: | 2024-07-30 19:13 |
| Submitted by: | Bastos Costa, Davi |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We investigate the invertible and non-invertible symmetries of topological finite group gauge theories in general spacetime dimensions, where the gauge group can be Abelian or non-Abelian. We focus in particular on the 0-form symmetry. The gapped domain walls that generate these symmetries are specified by boundary conditions for the gauge fields on either side of the wall. We investigate the fusion rules of these symmetries and their action on other topological defects including the Wilson lines, magnetic fluxes, and gapped boundaries. We illustrate these constructions with various novel examples, including non-invertible electric-magnetic duality symmetry in 3+1d $\mathbb{Z}_2$ gauge theory, and non-invertible analogs of electric-magnetic duality symmetry in non-Abelian finite group gauge theories. In particular, we discover topological domain walls that obey Fibonacci fusion rules in 2+1d gauge theory with dihedral gauge group of order 8. We also generalize the Cheshire string defect to analogous defects of general codimensions and gauge groups and show that they form a closed fusion algebra.
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:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)
Reports on this Submission
Strengths
1. The manuscript is very well written and easy to follow. The comprehensive review of finite gauge theory on the lattice is much appreciated.
2. The manuscript contains several interesting gapped domain walls, such as non-invertible EM duality with a Fibonacci-like fusion rule and generalized Cheshire strings.
Weaknesses
1. While the paper systematically computes and lists the fusion rules of gapped domain walls and their corresponding actions on gapped boundaries, the discussion on physical conclusions one can draw using these results is too brief.
Report
The authors provide a systematic presentation of the gapped domain walls in finite G gauge theories using the folding trick. They compute the fusion rules and the algebra of these gapped domain walls, as well as their actions on gapped boundary conditions. The results are easy to follow and presented pedagogically. The manuscript, as it stands, satisfies the journal's criteria and can be published.
My only suggestion is that it would be beneficial for the authors to add, if possible, an additional discussion on potential constraints when these gapped domain walls become symmetries. For instance, is the non-invertible EM duality anomalous?
I believe there is also a small typo on page 14. Using the convention in Eqs. (2.1) and (2.2), shouldn't the holonomy along the example path be $g_L g^{-1}_R h_R g_R g^{-1}_L h^{-1}_L$?
Recommendation
Publish (meets expectations and criteria for this Journal)
Strengths
1. Given the recent interest in non-invertible symmetries in the community, this work provides a timely addition to the literature.
2. The paper is written in a pedagogical way and can be easily followed.
Weaknesses
1. the result is systematic but not very surprising
2. the authors set some limitations on the defects they consider. For example, they restricted to untwisted gauge theories and considered a subclass of their defects. It would be nice if the authors can comment on why they made the restriction or what would be the main difficulty to extend the result in this paper to the more general case.
Report
This paper studies the co-dimension one defects in untwisted gauge theories with a finite gauge group. It presents a systematic analysis of possible defects, both invertible and non-invertible, and studied their fusion rule and action on topological excitations. An example of a higher codimensional defect -- the Cheshire string -- is also briefly discussed. The paper is carefully written and can be a good addition to the literature. I think the paper can be published as it is. I would appreciate if the authors can consider point 2 in the `weakness' list.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)