Abstract
The study of Coulomb branches of 3-dimensional \( \mathcal{N}=4 \) gauge theories via the associated Hilbert series, the so-called monopole formula, has been proven useful not only for 3-dimensional theories, but also for Higgs branches of 5 and 6-dimensional gauge theories with 8 supercharges. Recently, a conjecture connected different phases of 6-dimensional Higgs branches via gauging of a discrete global Sn symmetry. On the corresponding 3-dimensional Coulomb branch, this amounts to a geometric Sn-quotient. In this note, we prove the conjecture on Coulomb branches with unitary nodes and, moreover, extend it to Coulomb branches with other classical groups. The results promote discrete Sn-quotients to a versatile tool in the study of Coulomb branches.
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Hanany, A., Sperling, M. Discrete quotients of 3-dimensional \( \mathcal{N}=4 \) Coulomb branches via the cycle index. J. High Energ. Phys. 2018, 157 (2018). https://doi.org/10.1007/JHEP08(2018)157
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DOI: https://doi.org/10.1007/JHEP08(2018)157