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Generalized Symmetries and Anomalies of 3d N=4 SCFTs
by Lakshya Bhardwaj, Mathew Bullimore, Andrea E. V. Ferrari, Sakura Schafer-Nameki
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Lakshya Bhardwaj · Andrea Ferrari |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2301.02249v3 (pdf) |
| Date accepted: | 2024-02-28 |
| Date submitted: | 2024-01-26 19:20 |
| 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.
Author comments upon resubmission
To report 1:
Point 6: This is because the U(1) topological symmetries associated to unbalanced nodes neighbouring the balanced nodes contribute to the cartan of the non-abelian IR topological symmetry associated with the balanced nodes. This is a well-known phenomenon, and follows straightforwardly from the analysis of Gaiotto and Witten. A simple example of this phenomenon is exhibited already in eq (3.37).
List of changes
The changes suggested by the referees have been performed. The reference \cite{Benini:2018reh} has been added at the beginning of section 2.2.3
Published as SciPost Phys. 16, 080 (2024)