Abstract
We propose a family of IR dualities for 3d \( \mathcal{N} \) = 4 U(N) SQCD with Nf fundamental flavors and P Abelian hypermultiplets i.e. P hypermultiplets in the determinant representation of the gauge group. These theories are good in the Gaiotto-Witten sense if the number of fundamental flavors obeys the constraint Nf ≥ 2N − 1 with generic P ≥ 1, and in contrast to the standard U(N) SQCD, they do not admit an ugly regime. The IR dualities in question arise in the window Nf = 2N + 1, 2N, 2N − 1, with P = 1 in the first case and generic P ≥ 1 for the others. The dualities involving Nf = 2N ± 1 are characterized by an IR enhancement of the Coulomb branch global symmetry on one side of the duality, such that the rank of the emergent global symmetry group is greater than the rank of the UV global symmetry. The dual description makes the rank of this emergent global symmetry manifest in the UV. In addition, one can read off the emergent global symmetry itself from the dual quiver. We show that these dualities are related by certain field theory operations and assemble themselves into a duality web. Finally, we show that the U(N) SQCDs with Nf ≥ 2N − 1 and P Abelian hypers have Lagrangian 3d mirrors, and this allows one to explicitly write down the 3d mirror associated with a given IR dual pair. This paper is the first in a series of four papers on 3d \( \mathcal{N} \) = 4 Seiberg-like dualities.
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Acknowledgments
The author would like to thank Ibrahima Bah, Stefano Cremonesi, Amihay Hanany, Zohar Komargodski, Andrew Neitzke, Jaewon Song and Itamar Yaakov for discussion at different stages of the project. The author was supported in part at the Johns Hopkins University by the NSF grant PHY-2112699, and also by the Simons Collaboration on Global Categorical Symmetries, while this work was in preparation.
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Dey, A. Exploring Seiberg-like dualities with eight supercharges. J. High Energ. Phys. 2023, 167 (2023). https://doi.org/10.1007/JHEP10(2023)167
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DOI: https://doi.org/10.1007/JHEP10(2023)167