Construction and Deconstruction of Single Instanton Hilbert Series

Abstract

Many methods exist for the construction of the Hilbert series describing the moduli spaces of instantons. We explore some of the underlying group theoretic relationships between these various constructions, including those based on the Coulomb branches and Higgs branches of SUSY quiver gauge theories, as well as those based on generating functions derivable from the Weyl Character Formula. We show how the character description of the reduced single instanton moduli space of any Classical or Exceptional group can be deconstructed faithfully in terms of characters or modified Hall-Littlewood polynomials of its regular semi-simple subgroups. We derive and utilise Highest Weight Generating functions, both for the characters of Classical or Exceptional groups and for the Hall-Littlewood polynomials of unitary groups. We illustrate how the root space data encoded in extended Dynkin diagrams corresponds to relationships between the Coulomb branches of quiver gauge theories for instanton moduli spaces and those for T(SU(N)) moduli spaces.

97 pages, 12 figures

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Cited by in corpus (12)

• Magnetic quivers for rank 1 theories
• Quiver Theories for Moduli Spaces of Classical Group Nilpotent Orbits
• A slow review of the AGT correspondence
• Quiver Theories and Formulae for Nilpotent Orbits of Exceptional Algebras
• Magnetic quivers for rank 2 theories
• Folding Orthosymplectic Quivers
• Coulomb branches for rank 2 gauge groups in 3d N=4 gauge theories
• Hilbert series and mixed branches of $T[SU(N)]$ theory
• Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional N=4 theories
• Quotient Quiver Subtraction
• Highest Weight Generating functions for hyperKahler T*(G/H) spaces
• HWG for Coulomb branch of $3d$ Sicilian theory mirrors