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

TL;DR

This paper develops a method to compute equivariant Gromov-Witten invariants of orbifold spaces associated with finite groups by expressing them as sums over Feynman graphs, linking geometry, representation theory, and quantum Riemann-Roch.

Contribution

It introduces a novel approach to express equivariant Gromov-Witten invariants as sums over Feynman graphs using Tseng's orbifold quantum Riemann-Roch theorem.

Findings

Expressed invariants as sums over Feynman graphs

Connected descendant integrals with group representations

Provided a new computational framework for orbifold Gromov-Witten invariants

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 $G$.