SciPost Submission Page
Aspects of Categorical Symmetries from Branes: SymTFTs and Generalized Charges
by Fabio Apruzzi, Federico Bonetti, Dewi S.W. Gould, Sakura SchäferNameki
This is not the latest submitted version.
This Submission thread is now published as
Submission summary
Authors (as registered SciPost users):  Dewi Gould 
Submission information  

Preprint Link:  scipost_202310_00009v1 (pdf) 
Date submitted:  20231009 15:10 
Submitted by:  Gould, Dewi 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

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 socalled 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 noninvertible) 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 HananyWitten 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
Anonymous Report 2 on 2024422 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202310_00009v1, delivered 20240422, doi: 10.21468/SciPost.Report.8921
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 HananyWitten 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 nonclosed form such that it equals $\ell \Phi$, and then compute the integral of a wedge product involving this nonclosed 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 Mtheory". I was a bit surprised by this, since to my knowledge braneantibrane annihilation is poorly understood in Mtheory. Could the authors perhaps elaborate a bit on what they meant here?
Recommendation
Ask for minor revision
Anonymous Report 1 on 2024311 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202310_00009v1, delivered 20240311, doi: 10.21468/SciPost.Report.8690
Strengths
1The paper provides a systematic correspondence between the concepts in generalized symmetries (SymTFT, generalized charges, condensation defects 't Hooft anomaly) and string theory (Topological actions, Dbranes, HananyWitten move).
2The 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.
3The paper includes detailed tables and summary of topological actions in the appendix, which are useful for researchers who intend to do followups.
Weaknesses
1The 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
1In the actions with differential forms throughout this paper, sometimes a wedge product ^ is used and sometimes not. Please make the notations more consistent.
2The 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.
3In Table 3, the symmetry $\mathbb{Z}_{2,v}$ has no background gauge field, please write a short comment on this.
4In 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.