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.

55 pages and a number of figures

References in corpus (11)

• Sasaki-Einstein Manifolds and Volume Minimisation
• Mirrors of 3d Sicilian theories
• Generalized Superconformal Index for Three Dimensional Field Theories
• Down the rabbit hole with theories of class S
• Superconformal indices of three-dimensional theories related by mirror symmetry
• Counting Chiral Operators in Quiver Gauge Theories
• Coulomb branch Hilbert series and Hall-Littlewood polynomials
• Coulomb branch Hilbert series and Three Dimensional Sicilian Theories
• Hanany-Witten effect and SL(2,Z) dualities in matrix models
• Large N Free Energy of 3d N=4 SCFTs and AdS/CFT
• Describing codimension two defects

Cited by in corpus (27)

• Three-dimensional N=4 Linear Quivers and non-Abelian T-duals
• Magnetic Quivers, Higgs Branches, and 6d N=(1,0) Theories -- Orthogonal and Symplectic Gauge Groups
• 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
• Higgs Branches of U/SU Quivers via Brane Locking
• Conformal Manifolds and 3d Mirrors of Argyres-Douglas theories
• Magnetic quivers and negatively charged branes
• Mapping out the internal space in AdS/BCFT with Wilson loops
• Quiver Theories and Hilbert Series of Classical Slodowy Intersections
• Higgs, Coulomb, and Hall-Littlewood
• Hierarchies of RG flows in 6d $(1,0)$ massive E-strings
• Variations on S-fold CFTs
• 3d mirrors of the circle reduction of twisted $A_{2N}$ theories of class $\mathsf{S}$
• Nilpotent orbits and the Coulomb branch of $T^{\sigma }(G)$ theories: special orthogonal vs orthogonal gauge group factors
• Algebraic properties of the monopole formula
• Hilbert series and mixed branches of $T[SU(N)]$ theory
• Monopoles and dualities in $3d$ $\mathcal{N}=2$ quivers
• The Space of Vacua of 3d $\mathcal{N}=3$ Abelian Theories
• 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