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For any finite abelian group   $G$  , the equivariant Gromov–Witten invariants of   $[\mathbb {C}^r/G]$   can be viewed as a certain kind of abelian Hurwitz–Hodge integrals. In this paper, we use Tseng's orbifold quantum Riemann–Roch theorem to express this kind of abelian Hurwitz–Hodge integrals as a sum over Feynman graphs, where the weight of each graph is expressed in terms of descendant integrals over moduli spaces of stable curves and representations of   $G$  . This expression will play a crucial role in the proof of the remodeling conjecture for affine toric Calabi–Yau 3-orbifolds by the authors.

Equivariant Gromov–Witten Theory of Affine Smooth Toric Deligne–Mumford Stacks