Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
arXiv:1012.2725 · doi:10.1016/j.nuclphysb.2011.08.002
Abstract
We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analysing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver encodes the instanton dynamics of the noncommutative gauge theory, and is associated to the geometry of the singularity via the generalized McKay correspondence. The index of BPS states which compute the noncommutative Donaldson-Thomas invariants is realized via topological quantum mechanics based on the quiver data. We illustrate these constructions with several explicit examples, involving also higher rank Coulomb branch invariants and geometries with compact divisors, and connect our approach with other ones in the literature.
95 pages, 5 figures; v2: clarifying comments added, discussions using tilting strengthened, references added and updated; v3: minor corrections, final version to be published in Nuclear Physics B
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- ADHM in 8d, coloured solid partitions and Donaldson-Thomas invariants on orbifolds
- Tetrahedron instantons
- N=2 gauge theories, instanton moduli spaces and geometric representation theory
- The Origin of Calabi-Yau Crystals in BPS States Counting
- Crystal Melting, BPS Quivers and Plethystics
- Tetrahedron instantons in Donaldson-Thomas theory
- Noncommutative Instantons in Diverse Dimensions
- Quivers, Line Defects and Framed BPS Invariants
- On the M2-Brane Index on Noncommutative Crepant Resolutions
- Sasakian quiver gauge theories and instantons on cones over lens 5-spaces
- On Framed Quivers, BPS Invariants and Defects
- Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
- Attractor invariants, brane tilings and crystals
- BPS Spectra, Barcodes and Walls