A Vanishing Associated With Irregular Msp Fields

In [7] and [8], the notion of Mixed-Spin-P (MSP) fields is introduced and their C*-equivariant moduli space W-g,W-gamma,W-d is constructed. In this paper, we prove a vanishing of a class of localization terms in [(W-g,W-gamma,W-d)C*](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.