The moduli spaces of $3d$ $\mathcal{N}\ge 2$ Chern-Simons gauge theories and their Hilbert series

Abstract

We present a formula for the Hilbert series that counts gauge invariant chiral operators in a large class of 3d $\mathcal{N}\ge 2$ Yang-Mills-Chern-Simons theories. The formula counts 't Hooft monopole operators dressed by gauge invariants of a residual gauge theory of massless fields in the monopole background. We provide a general formula for the case of abelian theories, where nonperturbative corrections are absent, and consider a few examples of nonabelian theories where nonperturbative corrections are well understood. We also analyze in detail nonabelian ABJ(M) theories as well as worldvolume theories of M2-branes probing Calabi-Yau fourfold and hyperKähler twofold singularities with $\mathcal{N}=2$ and $\mathcal{N}=3$ supersymmetry.

72 pages + appendices

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Cited by in corpus (10)

• Lagrangians for generalized Argyres-Douglas theories
• Anomalies of Generalized Symmetries from Solitonic Defects
• Zero-form and one-form symmetries of the ABJ and related theories
• Dualities and flavored indices of M2-brane SCFTs
• Algebraic properties of the monopole formula
• 3d $\mathcal{N}=4$ mirror symmetry with 1-form symmetry
• Hilbert series and mixed branches of $T[SU(N)]$ theory
• The Space of Vacua of 3d $\mathcal{N}=3$ Abelian Theories
• Vacua, Symmetries, and Higgsing of Chern-Simons Matter Theories
• Semiclassics of three-dimensional SCFTs from holography