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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: | July 31, 2023, 4:38 p.m. |
| 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.
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Reports on this Submission
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Report #2 by Anonymous (Referee 1) 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
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 1) 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
Report
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.