Twisted Equivariant Gromov-Witten Theory of the Classifying Space of a Finite Group

Abstract

For any finite group $G$, the equivariant Gromov-Witten invariants of $[\mathbb{C}^r/G]$ can be viewed as a certain twisted Gromov-Witten invariants of the classifying stack $\mathcal{B} G$. In this paper, we use Tseng's orbifold quantum Riemann-Roch theorem to express the equivariant Gromov-Witten invariants of $[\mathbb{C}^r/G]$ 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 $G$.