A Vanishing Associated With Irregular MSP Fields

Abstract

Abstract In [ 7] and [ 8], the notion of Mixed-Spin-P (MSP) fields is introduced and their ${\mathbb{C}}^\ast $-equivariant moduli space ${{\mathcal{W}}}_{g,\gamma ,{\textbf d}}$ is constructed. In this paper, we prove a vanishing of a class of localization terms in $[(\mathcal{W}_{g,\gamma ,\mathbf{d}})^{\mathbb{C}^*}]^{\textrm{vir}}$, which implies the only quintic FJRW invariants that contribute to the relations derived from the theory of MSP fields are those with pure insertions $2/5$. It is critical in a proof of BCOV Feynman sum formula for quintic Calabi–Yau three-folds.