The orbifold topological vertex

We develop a topological vertex formalism for computing the Donaldson Thomas invariants of Calabi-Yau orbifolds. The basic combinatorial object is the orbifold vertex V(lambda mu nu)(G), a generating function for the number of 3D partitions asymptotic to 2D partitions lambda, mu, nu and colored by representations of a finite Abelian group G acting on C(3). In the case where G congruent to Z(n) acting on C(3) with transverse A(n-1) quotient singularities, we give an explicit formula for V(lambda mu nu)(G) 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 P(a,b)(I) and the local BZ(2) gerbe. (C) 2011 Elsevier Inc. All rights reserved.