Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-08-19
Physics
High Energy Physics
High Energy Physics - Theory
31 pages
Scientific paper
We summarize the main aspects of our recent construction of noncommutative Donaldson-Thomas invariants for abelian orbifold singularities via the enumeration of instanton solutions in a six-dimensional noncommutative N=2 gauge theory; this construction is based on the generalized McKay correspondence and identifies the instanton counting with the counting of framed representations of a quiver which is naturally associated to the geometry of the singularity. We extend these constructions to compute BPS partition functions for higher-rank refined and motivic noncommutative Donaldson-Thomas invariants in the Coulomb branch in terms of gauge theory variables and orbifold data. We introduce the notion of virtual instanton quiver associated with the natural symplectic charge lattice which governs the quantum wall-crossing behaviour of BPS states in this context. The McKay correspondence naturally connects our formalism with other approaches to wall-crossing based on quantum monodromy operators and cluster algebras.
Cirafici Michele
Sinkovics Annamaria
Szabo Richard J.
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