SciPost Submission Page
Composite subsystem symmetries and decoration of sub-dimensional excitations
by Avi Vadali, Zongyuan Wang, Arpit Dua, Wilbur Shirley, Xie Chen
Submission summary
| Authors (as registered SciPost users): | Xie Chen · Avi Vadali |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2312.04467v1 (pdf) |
| Date submitted: | 2024-01-26 03:21 |
| Submitted by: | Vadali, Avi |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
Flux binding is a mechanism that is well-understood for global symmetries. Given two systems, each with a global symmetry, gauging the composite symmetry instead of individual symmetries corresponds to the condensation of the composite of gauge charges belonging to individually gauged theories and the binding of the gauge fluxes. The condensed composite charge is created by a "short" string given by the new minimal coupling corresponding to the composite symmetry. This paper studies what happens when combined subsystem symmetries are gauged, especially when the component charges and fluxes have different sub-dimensional mobilities. We investigate $3+1$D systems with planar symmetries where, for example, the planar symmetry of a planon charge is combined with one of the planar symmetries of a fracton charge. We propose the principle of $\textit{Remote Detectability}$ to determine how the fluxes bind and potentially change their mobility. This understanding can then be used to design fracton models with sub-dimensional excitations that are decorated with excitations having nontrivial statistics or non-abelian fusion rules.
Current status:
Reports on this Submission
Report
This paper explores the gauge fluxes of gauge theories that arise from gauging different sub-symmetries of a global symmetry (subsystem 1 symmetry) x (subsystem 2 symmetry) x.... In particular, they show how the gauge fluxes that arise from gauging the entire symmetry group are related to those that arise by gauging diagonal subgroups. The paper is well organized and interesting to, at least, both the fracton/topological order community as well as the generalized symmetries community. I am therefore happy to recommend it for publication. However, I hope the authors will consider some of my comments and questions below, which could clarify parts of their paper and provide interesting questions for additions to this paper (or follow-up work).
Three questions I have regarding gauging:
1) How do the authors expect different types of gauging to affect their results (i.e., various types of twisted gauging implemented by conjugating with an SPT entangler before and after gauging)?
2) I believe the authors always assume the symmetry before gauging is not spontaneously broken (e.g., the starting model is a paramagnet). My understanding of why is that by gauging a non-SSB'd subsystem symmetry, you get a model with a dual subsystem symmetry that is SSB'd, which explains why you have subdimensional gauge charges. Do the authors know how things would change if their starting point differed, especially if the starting model was in a nontrivial SPT phase protected by the symmetry?
3 Do the authors know how the 't Hooft anomalies of the 0-form and subsystem symmetries affect their results? In particular, if the symmetry was anomalous and they gauged an anomaly-free subgroup, would they expect to get some sort of subsystem higher-groupoid or subsytem noninvertible symmetry?
For 2+1d abelian topological orders, the principle of remote detectability can be nicely stated in terms of 't Hooft anomalies of higher-form symmetries. Can the authors phrase their remote detectability principle using 't Hooft anomalies?
To improve clarify, could the authors distinguish between global and gauge symmetries, and global symmetry charges and gauge symmetry charges, more precisely in the introduction? I found the distinction clear in the main text and conclusion section, but I had difficulty following the terminology in the introduction. Relatedly, if the authors could clarify in the introduction what charges in which theory are being condensed (e.g., in the second paragraph), that would also make the introduction clearer.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)