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An Introduction to Higher-Form Symmetries
by Pedro R S Gomes
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Pedro Gomes |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202306_00015v1 (pdf) |
| Date accepted: | 2023-08-17 |
| Date submitted: | 2023-06-12 12:40 |
| Submitted by: | Gomes, Pedro |
| Submitted to: | SciPost Physics Lecture Notes |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
These notes are intended to be a pedagogical introduction to higher-form symmetries, which are symmetries whose charged objects are extended operators supported on lines, surfaces, and etc. This subject has been one of the most popular and effervescent topics of theoretical physics in recent years. Gauge theories are central in the study of higher-form symmetries, with Wilson and 't Hooft operators corresponding to the charged objects. Along these notes, we discuss in detail some basic aspects, including Abelian Maxwell and Chern-Simons theories, and $SU(N)$ non-Abelian gauge theories. We also discuss spontaneous breaking of higher-form symmetries.
Published as SciPost Phys. Lect. Notes 74 (2023)
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2023-8-1 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202306_00015v1, delivered 2023-08-01, doi: 10.21468/SciPost.Report.7591
Strengths
This is a very accessible review of higher form symmetries which goes carefully through the basics.
Weaknesses
The review contains very few interesting applications of the notion of higher-form symmetries.
Report
Since higher form symmetries have enjoyed a lot of popularity, both in the high energy and condensed matter literature, this elementary introduction is useful for beginning graduate students. I believe that the criteria for SciPost Lecture Notes are met.