ADHM in 8d, coloured solid partitions and Donaldson-Thomas invariants on orbifolds

Abstract

We study the moduli space of $SU(4)$ invariant BPS conditions in supersymmetric gauge theory on non-commutative ${\mathbb{C}}^4$ by means of an ADHM-like quiver construction and we classify the invariant solutions under the natural toric action in terms of solid partitions. In the orbifold case ${\mathbb{C}}^4/G$, $G$ being a finite subgroup of $SU(4)$, the classification is given in terms of coloured solid partitions. The statistical weight for their counting is defined through the associated equivariant cohomological gauge theory. We explicitly compute its partition function on ${\mathbb{C}}^4$ and ${\mathbb{C}}^2\times \left({\mathbb{C}}^2/{\mathbb{Z}}_2\right)$ which conjecturally provides the corresponding orbifold Donaldson-Thomas invariants.

42 pages. Comments are very welcome

References in corpus (4)

• Bases in coset conformal field theory from AGT correspondence and Macdonald polynomials at the roots of unity
• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics
• N=2 quiver gauge theories on A-type ALE spaces
• Crepant resolutions and Hilb^G(C^4) for certain abelian subgroups for SL(4,C)

Cited by in corpus (12)

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• The Origin of Calabi-Yau Crystals in BPS States Counting
• Gauge origami and quiver W-algebras
• Tetrahedron instantons in Donaldson-Thomas theory
• Double Quiver Gauge Theory and BPS/CFT Correspondence
• On the M2-Brane Index on Noncommutative Crepant Resolutions
• Charging solid partitions
• Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters
• A Donaldson-Thomas crepant resolution conjecture on Calabi-Yau 4-folds
• Tunnels Under Geometries (or Instantons Know Their Algebras)
• Gauge origami and quiver W-algebras IV: Pandharipande--Thomas $qq$-characters
• Charge functions for odd dimensional partitions