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Aspects of Categorical Symmetries from Branes: SymTFTs and Generalized Charges
by Fabio Apruzzi, Federico Bonetti, Dewi S.W. Gould, Sakura Schäfer-Nameki
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Dewi Gould |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202310_00009v2 (pdf) |
| Date accepted: | 2024-06-26 |
| Date submitted: | 2024-06-07 07:56 |
| Submitted by: | Gould, Dewi |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Recently it has been observed that branes in geometric engineering and holography have a striking connection with generalized global symmetries. In this paper we argue that branes, in a certain topological limit, not only furnish the symmetry generators, but also encode the so-called Symmetry Topological Field Theory (or SymTFT). For a $d$-dimensional QFT, this is a $(d+1)$-dimensional topological field theory, whose topological defects encode both the symmetry generators (invertible or non-invertible) and the generalized charges. Mathematically, the topological defects form the Drinfeld center of the symmetry category of the QFT. In this paper we derive the SymTFT and the Drinfeld center topological defects directly from branes. Central to the identification of these are Hanany-Witten brane configurations, which encode both topological couplings in the SymTFT and the generalized charges under the symmetries. We exemplify the general analysis with examples of QFTs realized in geometric engineering or holography.
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
Author comments upon resubmission
Referree 1. In response to the comment about the wedge product notation, we have fixed these inconsistencies throughout the draft and added comments where the wedge symbols are suppressed in the interest of clarity. In response to the comment about $2\pi$ normalizations, we have added a short comment below (2.3). In response to the comment about the vector symmetry background field, we have added a comment in the caption of Table 3. In response to the comment about $M_{p,q}$ notation we have fixed the typos above and below (4.38).
Referee 2. We thank the reviewer for this comment. We have added a clarifying footnote on page 28. We have fixed this typo. In response to this comment we have added an explicit computation around equation (3.52) and a footnote.
Published as SciPost Phys. 17, 025 (2024)
Reports on this Submission
Report #3 by Anonymous (Referee 1) on 2024-6-20 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202310_00009v2, delivered 2024-06-20, doi: 10.21468/SciPost.Report.9271
Strengths
1- The authors give a general and unified recipe of the construction of SymTFT from either geometric engineering or holography.
2- The democratic formulation summarized in section 3 is illuminating and is a very useful tool in the construction of SymTFT.
3- The different sources of BF-couplings and anomalies have been classified and examplified in a very clear way.
4- The interplay between (generalized) symmetries and charges as incarnation of Hanany-Witten effects between branes is accounted for in a very clear way.
Weaknesses
1- In textbooks (Becker&Becker&Schwarz and Polchinski) the fields that satisfy Bianchi identities are denoted by \tilde{F} while F = dC. The authors did not try to make such notational distinction, which I understand that it greatly reduces clustering symbols, but could be a source of confusion.
Report
This work is an important step in understanding the construction of SymTFT from either geometric engineering or holography. The authors proposed a useful toolbox that enables both the construction of a large class of SymTFTs and the analysis of the various interplays between the symmetries and the charges. The mathematical tools (mostly differential forms) used in and the physical intuition (Hanany-Witten effects) behind this paper are surprisingly simple (in a good way), yet the consequences they lead to are profound. The topic, and the quality of paper, are well-suited for SciPost Phys, and I recommend for publication once a few typos are corrected.
Requested changes
1- Typo: RHS of (2.11), the superscript might be (i)?
2- Typo: (2.13), wrong place of \hat
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)