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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
Submission summary
| Authors (as registered SciPost users): | Dewi Gould |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202310_00009v1 (pdf) |
| Date submitted: | 2023-10-09 15:10 |
| 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.
Current status:
Reports on this Submission
Strengths
1- The paper advances the program of connecting the categorical description of symmetries with considerations of holography/geometric engineering.
2- The discussion is clear and many examples are given.
Weaknesses
1- Some points of the formalism are not clearly explained.
Report
This is an interesting paper on symmetries and holography/geometric engineering. The main motivation of the paper is to reinforce the connection between branes and symmetries.
This is a connection that had already been pointed out in a number of papers before (including by some of the authors of the current paper), but the current paper makes some new progress, particularly in the analysis of the connection between the Hanany-Witten effect and some aspect of categorical symmetries.
Overall this is a good paper, and I recommend publication after the minor comments below are addressed.
Requested changes
1- I don't think I understand how the linking pairings are to be computed in practice. As far as I understand, we are instructed to find a non-closed form such that it equals $\ell \Phi$, and then compute the integral of a wedge product involving this non-closed form. I have no issue with the discussion abstractly, but in practice I wouldn't know how to do this calculation. Perhaps the authors could work out an example or two explicitly, to show the interested reader how this works in detail? (Some simple geometry like $S^3/\mathbf{Z}_n$ and/or perhaps eq. (3.115) for $\mathbb{RP}^5$ would be ideal, if possible.) I apologize in advance in the likely case that this is explained in some of the references they cite, but even in this case a short summary and an example or two would greatly benefit the reader.
2- There's a typo above (3.126), where it says "souces".
3- At the beginning of section 3.6, where condensation defects are studied, the authors say "For definiteness we work in type II, but similar remarks apply to M-theory". I was a bit surprised by this, since to my knowledge brane-anti-brane annihilation is poorly understood in M-theory. Could the authors perhaps elaborate a bit on what they meant here?
Recommendation
Ask for minor revision
Strengths
1-The paper provides a systematic correspondence between the concepts in generalized symmetries (SymTFT, generalized charges, condensation defects 't Hooft anomaly) and string theory (Topological actions, D-branes, Hanany-Witten move).
2-The paper contains many concrete examples, including 4d N=4 so(4n) and su(n) SYM, 4d N=2 and N=1 models. The discussions are very explicit.
3-The paper includes detailed tables and summary of topological actions in the appendix, which are useful for researchers who intend to do follow-ups.
Weaknesses
1-The notations in formula are not completely consistent.
Report
This paper provided detailed realizations of the novel concepts in generalized symmetries, such as SymTFT, condensation defects and generalized charges, in the geometric/brane setups in string theory. The significance of this paper is twofold: (1) it provides a new perspective to interpret these generalized symmetry concepts; (2) it inspires researchers to think about string theory in a categorical framework.
I think this paper definitely meets the standard of SciPost Physics, and should be published after a minor revision.
Requested changes
1-In the actions with differential forms throughout this paper, sometimes a wedge product ^ is used and sometimes not. Please make the notations more consistent.
2-The SymTFT actions used throughout the paper, starting from (2.3), differs from the usual conventions by a factor of $2\pi$, please comment on this point.
3-In Table 3, the symmetry $\mathbb{Z}_{2,v}$ has no background gauge field, please write a short comment on this.
4-In the formula before and after (4.38): $M=M_{p_1,q_1}\dots$, some terms are with comma and some are not, please make it more consistent.