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Generalized Symmetries and Anomalies of 3d N=4 SCFTs
by Lakshya Bhardwaj, Mathew Bullimore, Andrea E. V. Ferrari, Sakura Schäfer-Nameki
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Submission summary
| Authors (as registered SciPost users): | Lakshya Bhardwaj · Andrea Ferrari |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2301.02249v2 (pdf) |
| Date submitted: | 2023-07-31 16:38 |
| Submitted by: | Ferrari, Andrea |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study generalized global symmetries and their 't Hooft anomalies in 3d N=4 superconformal field theories (SCFTs). Following some general considerations, we focus on good quiver gauge theories, comprised of balanced unitary nodes and unbalanced unitary and special unitary nodes. While the global form of the Higgs branch symmetry group may be determined from the UV Lagrangian, the global form of Coulomb branch symmetry groups and associated mixed 't Hooft anomalies are more subtle due to potential symmetry enhancement in the IR. We describe how Coulomb branch symmetry groups and their mixed 't Hooft anomalies can be deduced from the UV Lagrangian by studying center charges of various types of monopole operators, providing a concrete and unambiguous way to implement 't Hooft anomaly matching. The final expression for the symmetry group and 't Hooft anomalies has a concise form that can be easily read off from the quiver data, specifically from the positions of the unbalanced and flavor nodes with respect to the positions of the balanced nodes. We provide consistency checks by applying our method to compute symmetry groups of 3d N=4 theories corresponding to magnetic quivers of 4d Class S theories and 5d SCFTs. We are able to match these results against the flavor symmetry groups of the 4d and 5d theories computed using independent methods. Another strong consistency check is provided by comparing symmetry groups and anomalies of two theories related by 3d mirror symmetry.
Current status:
Reports on this Submission
Report
This article serves as a useful reference on generalized global symmetries and 't Hooft anomalies in 3d $\mathcal{N}=4$ SCFTs. It contains many explicit results with clear explanations. The referee sees that the discussion on the $U(1)$ gauge theory with hypermultiplets of charge $q$ has been improved significantly from the first version on the arXiv. In the referee's opinion, it deserves publication after minor correction suggested by the other referees.
Report #2 by Anonymous (Referee 4) on 2023-10-8 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2301.02249v2, delivered 2023-10-08, doi: 10.21468/SciPost.Report.7911
Report
There are additional grammatical typos:
Requested changes
1- At the beginning of p.18: The symmetries are summarises as follows $\to$ The symmetries are summarised as follows
2- At the end of p.31: transforming in same representations $\to$ transforming in \emph{the} same representations. Even below there are many places that miss \emph{the} in front of same
3- Above (3.67): is is $\to$ is
4- Below (6.21): this non-genuine local operator needs to attached to $\to$ this non-genuine local operator needs to \emph{be} attached to
5- In p.66: The intersection pattern of the $(-2,0)$ curves give $\to$ The intersection pattern of the $(-2,0)$ curves gives
6- Above (A.4): The affect of this blowdown $\to$ The effect of this blowdown
Report #1 by Anonymous (Referee 5) on 2023-10-8 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2301.02249v2, delivered 2023-10-08, doi: 10.21468/SciPost.Report.7910
Strengths
The paper is a well-structured, detailed, and strong contribution to the study of generalized symmetries and 't Hooft anomalies in 3d \( \mathcal{N}=4 \) SCFTs. The technical depth, combined with solid consistency checks, makes it an important work in the area. After the following points are addressed, I believe the paper would be a good fit for publication in SciPost.
Report
The manuscript presents a thorough study of generalized global symmetries and their 't Hooft anomalies in 3d \(\mathcal{N}=4\) superconformal field theories (SCFTs). An essential feature of this study is the method used to deduce generalized symmetries and their anomalies for the Coulomb branch from the UV Lagrangian. The primary focus of the study is on good quiver gauge theories with (special) unitary gauge groups. As a concrete example, the T[SU(\(n\))] theories are first studied from this viewpoint in great details. Then, more general quiver theories are considered. The authors make their results even more concrete by presenting various consistency checks, using magnetic quiver techniques.
Requested changes
1- The paper \cite{Benini:2018reh} is one of the pioneering papers which provide a detailed examination of 2-groups and their 't Hooft anomalies. It is important to cite this work.
2- The hat notation appears first in Eqn.(2.10), which is supposed to indicate the Pontryagin dual. This notation should be mentioned.
3- In the first line of the first bullet in p.11, $\lambda_j=0$ is supposed to be $m_j=0$.
4- Below Eqn.(4.11), oft-called $\to$ so-called
5- Above Eqn.(4.13): "The charge $q_i$ of $O$ under $U(1)_i$ for $i\in \mathcal {U}$ is $n_i$" $\to$ "The charge of $O$ under $U(1)_i$ for $i\in \mathcal {U}$ is $q_i$". Anyhow, the use of $n_i$ should be avoided since it is used as a rank of a unitary group right below.
6- Eqn.(4.13) gives the definition of Dynkin coefficients for topological symmetry $\mathfrak{f}_a$. It is unclear why it involves the summation over unbalanced unitary nodes in $\mathcal{U}$. The reason needs to be elaborated. If it is a typo, it should be corrected.