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.

arXiv comment42 pages. Comments are very welcome

References in corpus (30)

• Instantons on noncommutative R^4, and (2,0) superconformal six dimensional theory
• Quantum Foam and Topological Strings
• Special Quantum Field Theories In Eight And Other Dimensions
• Instantons on Noncommutative R^4 and Projection Operators
• BPS Bound States Of D0-D6 And D0-D8 Systems In A B-Field
• Multi instanton calculus on ALE spaces
• Euclidean SYM Theories by Time Reduction and Special Holonomy Manifolds
• Higher Dimensional Analogues of Donaldson-Witten Theory
• Gauge Theories on ALE Space and Super Liouville Correlation Functions
• Instanton moduli spaces and bases in coset conformal field theory
• Vortex partition functions, wall crossing and equivariant Gromov-Witten invariants
• Virtual fundamental classes for moduli spaces of sheaves on Calabi-Yau four-folds
• Magnificent Four with Colors
• Zero-dimensional Donaldson-Thomas invariants of Calabi-Yau 4-folds
• Conifold Transitions in M-theory on Calabi-Yau Fourfolds with Background Fluxes
• Bases in coset conformal field theory from AGT correspondence and Macdonald polynomials at the roots of unity
• Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-folds
• Donaldson-Thomas theory for Calabi-Yau 4-folds
• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics
• N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae
• Orientability for gauge theories on Calabi-Yau manifolds
• The Stringy Instanton Partition Function
• Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
• Topological Vector Symmetry of BRSTQFT and Construction of Maximal Supersymmetry
• N=2 quiver gauge theories on A-type ALE spaces
• Ratliff-Rush Monomial Ideals
• ADHM construction of perverse instanton sheaves
• Commuting matrices and the Hilbert scheme of points on affine spaces
• On the existence of crepant resolutions of Gorenstein Abelian quotient singularities in dimensions \geq 4
• Crepant resolutions and Hilb^G(C^4) for certain abelian subgroups for SL(4,C)

Cited by in corpus (12)

• Tetrahedron instantons
• 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