Hilbert series and mixed branches of $T[SU(N)]$ theory

Abstract

We consider mixed branches of 3d $\mathcal{N}=4$ $T[SU(N)]$ theory. We compute the Hilbert series of the Coulomb branch part of the mixed branch from a restriction rule acting on the Hilbert series of the full Coulomb branch that will truncate the magnetic charge summation only to the subset of BPS dressed monopole operators that arise in the Coulomb branch sublocus where the mixed branch stems. This restriction can be understood directly from the type IIB brane picture by a relation between the magnetic charges of the monopoles and brane position moduli. We also apply the restriction rule to the Higgs branch part of a given mixed branch by exploiting 3d mirror symmetry. Both cases show complete agreement with the results calculated by different methods.

44 pages, 26 figures, 5 tables

References in corpus (11)

• Supersymmetry enhancement by monopole operators
• SQCD: A Geometric Apercu
• Coulomb Branch and The Moduli Space of Instantons
• T^σ_ρ(G) Theories and Their Hilbert Series
• Coulomb branch Hilbert series and Hall-Littlewood polynomials
• Coulomb branch Hilbert series and Three Dimensional Sicilian Theories
• The Coulomb Branch of 3d $\mathcal{N}=4$ Theories
• The moduli spaces of $3d$ $\mathcal{N}\ge 2$ Chern-Simons gauge theories and their Hilbert series
• Counting BPS Operators in the Chiral Ring of N=2 Supersymmetric Gauge Theories or N=2 Braine Surgery
• The moduli space of vacua of N=2 class S theories
• Examples of global symmetry enhancement by monopole operators

Cited by in corpus (1)

• Algebraic properties of the monopole formula