T^σ_ρ(G) Theories and Their Hilbert Series

Abstract

We give an explicit formula for the Higgs and Coulomb branch Hilbert series for the class of 3d N=4 superconformal gauge theories T^σ_ρ(G) corresponding to a set of D3 branes ending on NS5 and D5-branes, with or without O3 planes. Here G is a classical group, σis a partition of G and ρa partition of the dual group G^\vee. In deriving such a formula we make use of the recently discovered formula for the Hilbert series of the quantum Coulomb branch of N=4 superconformal theories. The result can be expressed in terms of a generalization of a class of symmetric functions, the Hall-Littlewood polynomials, and can be interpreted in mathematical language in terms of localization. We mainly consider the case G=SU(N) but some interesting results are also given for orthogonal and symplectic groups.

arXiv comment55 pages and a number of figures

References in corpus (34)

• An Index for 4 dimensional Super Conformal Theories
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Mirror Symmetry in Three Dimensional Gauge Theories
• Type IIB Superstrings, BPS Monopoles, And Three-Dimensional Gauge Dynamics
• Counting chiral primaries in N=1 d=4 superconformal field theories
• The Moduli Space of N=2 SUSY QCD and Duality in N=1 SUSY QCD
• Gauge Theories and Macdonald Polynomials
• The complete superconformal index for N=6 Chern-Simons theory
• Sasaki-Einstein Manifolds and Volume Minimisation
• Index for three dimensional superconformal field theories with general R-charge assignments
• Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories
• Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories
• Mirrors of 3d Sicilian theories
• Bootstrapping the superconformal index with surface defects
• Sicilian gauge theories and N=1 dualities
• Holographic Duals of D=3 N=4 Superconformal Field Theories
• Generalized Superconformal Index for Three Dimensional Field Theories
• Superconformal indices of three-dimensional theories related by mirror symmetry
• Down the rabbit hole with theories of class S
• Exceptional Indices
• Counting Chiral Operators in Quiver Gauge Theories
• 3d Partition Function as Overlap of Wavefunctions
• Coulomb branch Hilbert series and Hall-Littlewood polynomials
• Coulomb branch Hilbert series and Three Dimensional Sicilian Theories
• Counting BPS Baryonic Operators in CFTs with Sasaki-Einstein duals
• Mirror symmetry by O3-planes
• N=2 Moduli Spaces and N=1 Dualities for SO(n_c) and USp(2n_c) SuperQCD
• Symplectic Resolutions for Nilpotent Orbits
• Hanany-Witten effect and SL(2,Z) dualities in matrix models
• Baryonic Generating Functions
• Large N Free Energy of 3d N=4 SCFTs and AdS/CFT
• Higgs branch, HyperKahler quotient and duality in SUSY N=2 Yang-Mills theories
• Mirror Symmetry in Three Dimensions via Gauged Linear Quivers
• Describing codimension two defects

Cited by in corpus (55)

• Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal{N}=4$ gauge theories, II
• Comments on twisted indices in 3d supersymmetric gauge theories
• Vertex operator algebras, Higgs branches, and modular differential equations
• Quiver Subtractions
• Three-dimensional N=4 Linear Quivers and non-Abelian T-duals
• Quiver Theories for Moduli Spaces of Classical Group Nilpotent Orbits
• Magnetic Quivers, Higgs Branches, and 6d N=(1,0) Theories -- Orthogonal and Symplectic Gauge Groups
• Branes and the Kraft-Procesi transition: classical case
• T-branes, Anomalies and Moduli Spaces in 6D SCFTs
• Partition functions of 3d $\hat{D}$-quivers and their mirror duals from 1d free fermions
• Quiver Theories and Formulae for Nilpotent Orbits of Exceptional Algebras
• Hasse Diagrams for $3d$ $\mathcal{N}=4$ Quiver Gauge Theories -- Inversion and the full Moduli Space
• Folding Orthosymplectic Quivers
• The moduli spaces of $3d$ $\mathcal{N}\ge 2$ Chern-Simons gauge theories and their Hilbert series
• The Infrared Fixed Points of 3d $\mathcal{N}=4$ $USp(2N)$ SQCD Theories
• Conformal Manifolds and 3d Mirrors of Argyres-Douglas theories
• Higgs Branches of U/SU Quivers via Brane Locking
• Discrete quotients of 3-dimensional N = 4 Coulomb branches via the cycle index
• Coulomb branches for rank 2 gauge groups in 3d N=4 gauge theories
• Mapping out the internal space in AdS/BCFT with Wilson loops
• Magnetic quivers and negatively charged branes
• T-branes, monopoles and S-duality
• The moduli spaces of S-fold CFTs
• Quiver Theories and Hilbert Series of Classical Slodowy Intersections
• Mirror theories of 3d $\mathcal{N}=2$ SQCD
• Higgs, Coulomb, and Hall-Littlewood
• Quiver Theories and Formulae for Slodowy Slices of Classical Algebras
• Ungauging Schemes and Coulomb Branches of Non-simply Laced Quiver Theories
• Hierarchies of RG flows in 6d $(1,0)$ massive E-strings
• Variations on S-fold CFTs
• Nilpotent orbits and the Coulomb branch of $T^{\sigma }(G)$ theories: special orthogonal vs orthogonal gauge group factors
• 3d mirrors of the circle reduction of twisted $A_{2N}$ theories of class $\mathsf{S}$
• 4d N=1 from 6d N=(1,0) on a torus with fluxes
• Factorisation of 3d $\mathcal{N}=4$ Twisted Indices and the Geometry of Vortex Moduli Space
• Algebraic properties of the monopole formula
• Hilbert series and mixed branches of $T[SU(N)]$ theory
• Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional N=4 theories
• Minimally Unbalanced Quivers
• Ring Relations and Mirror Map from Branes
• Marginal Deformations of 3d N=4 Linear Quiver Theories
• Little String Origin of Surface Defects
• Monopoles and dualities in $3d$ $\mathcal{N}=2$ quivers
• The Space of Vacua of 3d $\mathcal{N}=3$ Abelian Theories
• Masses, Sheets and Rigid SCFTs
• Moduli space singularities for $3d$ $\mathcal{N}=4$ circular quiver gauge theories
• Highest Weight Generating functions for hyperKahler T*(G/H) spaces
• Quantized Coulomb Branches, Monopole Bubbling and Wall-Crossing Phenomena in 3d $\mathcal{N}=4$ Theories
• $D_n$ Dynkin quiver moduli spaces
• Towards Deconstruction of the Type D (2,0) Theory
• Quiver Polymerisation
• The Hilbert series of 3d N=2 Yang-Mills theories with vectorlike matter
• Holomorphic boundary conditions for topological field theories via branes in twisted supergravity
• On the planar limit of 3d $T_{\rho }^{\sigma }[SU(N)]$
• Coulomb Branch for A-type Balanced Quivers in 3d $\mathcal{N}=4$ gauge theories
• HWG for Coulomb branch of $3d$ Sicilian theory mirrors