SciPost Submission Page
Fractons on curved spacetime in 2 + 1 dimensions
by Jelle Hartong, Giandomenico Palumbo, Simon Pekar, Alfredo Perez, Stefan Prohazka
Submission summary
| Authors (as registered SciPost users): | Alfredo Perez · Stefan Prohazka |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202409_00027v1 (pdf) |
| Date submitted: | 2024-09-22 00:47 |
| Submitted by: | Perez, Alfredo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study dipole Chern--Simons theory with and without a cosmological constant in $2+1$ dimensions. We write the theory in a second order formulation and show that this leads to a fracton gauge theory coupled to Aristotelian geometry which can also be coupled to matter. This coupling exhibits the remarkable property of generalizing dipole gauge invariance to curved spacetimes, without placing any limitations on the possible geometries. We also use the second order formulation to construct a higher dimensional generalization of the action. Finally, for the $(2+1)$-dimensional Chern--Simons theory we find solutions and interpret these as electric monopoles, analyze their charges and argue that the asymptotic symmetries are infinite-dimensional.
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
Strengths
1- Clear and well-defined goals, which are achieved
2- Excellent presentation
3- Topical research subject
Weaknesses
None
Report
The paper studies a specific Chern-Simons theory that has an interpretation in terms of fractons. While Chern-Simons theories are of course well-known and -studied, they offer a rich variety of physical systems depending on the choice of gauge group and boundary conditions, ranging from Quantum Hall physics to gravity. The present work picks an interesting intermediate spot that has both a gravity- and a cond-mat flavour. In particular, they chose the fracton algebra (2.1) as gauge algebra and proceed from there.
The techniques to study this theory are well-established, so in purely technical terms the papers offers no surprises. However, the novel and surprising aspect uncovered in their work are the specific features of the fracton gauge theory, its various extensions (e.g. to include a cosmological constant), and its asymptotic symmetry analysis.
The discussion section offers a perspective to further extensions and applications, and while one might lament that none such applications are addressed in this work, in my opinion the paper has enough meat to stand on its own, and its broad scope does not require specific examples of detailed applications.
In terms of research topic, style of presentation, and originality the paper is suitable for publication in SciPost Physics in its present form. Therefore, I suggest its publication in its present form.
Requested changes
None
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Report #1 by Mariano Cadoni (Referee 1) on 2024-11-4 (Invited Report)
Strengths
1. The algebraic structure, the formal derivation and in general the whole mathematical setup is well described and organized.
Weaknesses
2. Physical aspects and implications of the formalism are sometimes only sketched and not adequately discussed
Report
In this paper the authors discuss a non-relativistic version of Chern-Simon theory. The paper is well organized and clearly written. The results are of interest for several ares of gravitational physics an potentially may open the way to cross fertilization between the areas of gravitational and condensed matter physics. I recommend publication after the authors have considered my comments below.
Requested changes
1. The equivalence between the Chern-Simon (CS) and geometric formulation of the theory should be discussed not only from the formal but also from the physical point of view. This is particularly needed because differently from usual CS theory they do not have the full relativistic symmetries so that the physical meaning of the 3D gravity theory (3.29) is not completely clear. Some points are addressed in Sect. (3.4), but it is not enough.
2. As stated by the author there is an interesting relation between the circularly symmetric solutions of the theory and the BTZ black hole. This includes the notion of asymptotic symmetry, which in the relativistic case is at the heart of the AdS_3/CFT_2 correspondence (see the famous Brown & Henneaux paper) and of Strominger's microscopic derivation of the entropy of the BTZ black hole.
It would be nice if the authors could at least comment on the possibility to extend this correspondence and related entropy computation to the nonrelativistic case under consideration.
Recommendation
Ask for minor revision