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.

arXiv comment72 pages + appendices

References in corpus (64)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Mirror Symmetry in Three Dimensional Gauge Theories
• Fractional M2-branes
• Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions
• Branes, Superpotentials and Superconformal Fixed Points
• On Mirror Symmetry in Three Dimensional Abelian Gauge Theories
• Topological Disorder Operators in Three-Dimensional Conformal Field Theory
• Index for three dimensional superconformal field theories with general R-charge assignments
• Mirror Symmetry in Three-Dimensional Gauge Theories, Quivers and D-branes
• The Geometric Dual of a-maximisation for Toric Sasaki-Einstein Manifolds
• Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories
• Comments on 3d Seiberg-like dualities
• N=4 Superconformal Chern-Simons Theories with Hyper and Twisted Hyper Multiplets
• Monopole Operators and Mirror Symmetry in Three Dimensions
• Dynamics of N=2 Supersymmetric Gauge Theories in Three Dimensions
• On the moduli space of elliptic Maxwell-Chern-Simons theories
• Aspects of 3d N=2 Chern-Simons-Matter Theories
• Tilings, Chern-Simons Theories and M2 Branes
• On the Moduli Space of the Cascading SU(M+p)xSU(p) Gauge Theory
• The Master Space of N=1 Gauge Theories
• Brane Tilings and M2 Branes
• The Hilbert Series of the One Instanton Moduli Space
• Chiral flavors and M2-branes at toric CY4 singularities
• Supersymmetry enhancement by monopole operators
• 3D superconformal theories from Sasakian seven-manifolds: new nontrivial evidences for AdS_4/CFT_3
• SQCD: A Geometric Apercu
• A simple class of N=3 gauge/gravity duals
• The gauge dual of Romans mass
• Down the rabbit hole with theories of class S
• Charge Lattices and Consistency of 6D Supergravity
• Branes and Supersymmetry Breaking in Three Dimensional Gauge Theories
• Notes on adding D6 branes wrapping RP3 in AdS4 x CP3
• Coulomb Branch and The Moduli Space of Instantons
• Notes on toric Sasaki-Einstein seven-manifolds and AdS_4/CFT_3
• A note on the holographic interpretation of string theory backgrounds with varying flux
• A note on the holography of Chern-Simons matter theories with flavour
• T^σ_ρ(G) Theories and Their Hilbert Series
• Monopole operators in three-dimensional N=4 SYM and mirror symmetry
• Quantum moduli space of Chern-Simons quivers, wrapped D6-branes and AdS4/CFT3
• M-Theory Origin of Mirror Symmetry in Three Dimensional Gauge Theories
• Coulomb branch Hilbert series and Hall-Littlewood polynomials
• Branes, Instantons, And Taub-NUT Spaces
• AdS_4/CFT_3 duals from M2-branes at hypersurface singularities and their deformations
• Argyres-Seiberg duality and the Higgs branch
• Coulomb branch Hilbert series and Three Dimensional Sicilian Theories
• Dynamics of N=2 Supersymmetric Chern-Simons Theories
• Counting BPS Baryonic Operators in CFTs with Sasaki-Einstein duals
• Highest Weight Generating Functions for Hilbert Series
• Mirror Symmetry and Toric Geometry in Three-Dimensional Gauge Theories
• Mirror Symmetry in 2+1 and 1+1 Dimensions
• Counting Gauge Invariant Operators in SQCD with Classical Gauge Groups
• Hanany-Witten effect and SL(2,Z) dualities in matrix models
• Complete Intersection Moduli Spaces in N=4 Gauge Theories in Three Dimensions
• Baryonic Generating Functions
• Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n
• Type IIB construction of flavoured ABJ(M) and fractional M2 branes
• Toric Fano varieties and Chern-Simons quivers
• Hilbert Series for Theories with Aharony Duals
• The moduli space of instantons on an ALE space from 3d $\mathcal{N}=4$ field theories
• Three Dimensional Mirror Symmetry and Partition Function on $S^3$
• New $Ad{S}_4\times X_7$ Geometries with $\mathcal{N}=6$ in M Theory
• D-branes Wrapped on Fuzzy del Pezzo Surfaces

Cited by in corpus (22)

• Lagrangians for generalized Argyres-Douglas theories
• Geometry of $\mathcal{I}$-extremization and black holes microstates
• The Infrared Physics of Bad Theories
• Anomalies of Generalized Symmetries from Solitonic Defects
• Zero-form and one-form symmetries of the ABJ and related theories
• Fundamental Vortices, Wall-Crossing, and Particle-Vortex Duality
• T-branes, monopoles and S-duality
• The moduli spaces of S-fold CFTs
• New 3d $\mathcal{N}=2$ SCFT's with $N^{3/2}$ scaling
• Dualities and flavored indices of M2-brane SCFTs
• Algebraic properties of the monopole formula
• 3d $\mathcal{N}=4$ mirror symmetry with 1-form symmetry
• New 3d $\mathcal{N}=2$ Dualities from Quadratic Monopoles
• Hilbert series and mixed branches of $T[SU(N)]$ theory
• Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional N=4 theories
• Marginal Deformations of 3d N=4 Linear Quiver Theories
• The Space of Vacua of 3d $\mathcal{N}=3$ Abelian Theories
• Moduli space singularities for $3d$ $\mathcal{N}=4$ circular quiver gauge theories
• Standard Model Plethystics
• Quantized Coulomb Branches, Monopole Bubbling and Wall-Crossing Phenomena in 3d $\mathcal{N}=4$ Theories
• Vacua, Symmetries, and Higgsing of Chern-Simons Matter Theories
• Semiclassics of three-dimensional SCFTs from holography