The orbifold topological vertex

AbstractWe develop a topological vertex formalism for computing the Donaldson–Thomas invariants of Calabi–Yau orbifolds. The basic combinatorial object is the orbifold vertex VλμνG, a generating function for the number of 3D partitions asymptotic to 2D partitions λ, μ, ν and colored by representations of a finite Abelian group G acting on C3. In the case where G≅Zn acting on C3 with transverse An−1 quotient singularities, we give an explicit formula for VλμνG in terms of Schur functions. We discuss applications of our formalism to the Donaldson–Thomas crepant resolution conjecture and to the orbifold Donaldson–Thomas/Gromov–Witten correspondence. We also explicitly compute the Donaldson–Thomas partition function for some simple orbifold geometries: the local football Pa,b1 and the local BZ2 gerbe