Abstract
Discrete global symmetries of 4d \( \mathcal{N} \) = 2 SCFTs are studied via two operations: gauging and twisted compactification. We consider gauging of discrete symmetries in several well-known 4d \( \mathcal{N} \) = 2 SCFTs, including SU(n) SQCD with 2n flavors, theories of class \( \mathcal{S} \) of type A2n−1, and Argyres-Douglas theories of type (AN, AN), as well as propose new 4d SCFTs as a result. The wreathing technique, which involves gauging a subgroup of the automorphism group of the quiver diagram of the corresponding 3d mirror theory, is exploited. This allows us to understand several properties of discretely gauged theories, including moduli spaces and how discrete gauging affects the mixed ’t Hooft anomaly between the 1-form symmetry and the 0-form flavor symmetry. Many examples are viewed through the lens of the Argyres-Seiberg duality and its generalization. We also examine discrete gauging of SU(2) SQCD with 4 flavors by various ℤ2 and ℤ2 × ℤ2 subgroups of the permutation group S4 using the superconformal index. Regarding compactification, we propose a magnetic quiver for 4d \( \mathcal{N} \) = 2 SU(n) SQCD with 2n flavors compactified on a circle with a ℤ2 twist. The twisted compactification by non-invertible symmetries of the 4d \( \mathcal{N} \) = 4 SYM theory with gauge group SU(N) is revisited. The non-invertible symmetry naturally gives rise to a ℤk action on the scalar fields parametrizing the moduli space. Upon examining the ℤk invariant chiral ring of the Higgs branch, we find that, in addition to the largest branch of the moduli space that is expected to be captured by the ABJ(M) theory, there exist in general nilpotent operators that lead to a branch of the moduli space which is a radical ideal.
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Acknowledgments
The authors thank Federico Carta for the useful discussions and previous collaborations. We also thank Guillermo Arias-Tamargo, Craig Lawrie, and Thekla Lepper for helpful discussions on the computation of wreathed quivers, and Julius Grimminger for useful discussions on non-simply laced quivers and twisted compactifications. N. M. is grateful to Alessandro Tomasiello for various insightful discussions on twisted compactifications. The work of S. G. is supported by the INFN grant “Per attività di formazione per sostenere progetti di ricerca” (GRANT 73/STRONGQFT). W. H. thanks the Galileo Galilei Institute for Theoretical Physics for the hospitality and the INFN for partial support during the completion of this work. A. M. is supported in part by Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy EXC 2121 Quantum Universe 390833306 and Deutsche Forschungsgemeinschaft through a German-Israeli Project Cooperation (DIP) grant “Holography and the Swampland”.
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Giacomelli, S., Harding, W., Mekareeya, N. et al. Discrete global symmetries: gauging and twisted compactification. J. High Energ. Phys. 2024, 304 (2024). https://doi.org/10.1007/JHEP05(2024)304
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DOI: https://doi.org/10.1007/JHEP05(2024)304