A vanishing associated with irregular MSP fields

Abstract

In previous work, Mixed-Spin-P field has been introduced and their moduli space ${\mathcal{W}}_{g,\gamma ,\mathbf{d}}$ together with a ${\mathbb{C}}^{\ast }$ action is constructed. Applying virtual localization to their virtual classes $[{\mathcal{W}}_{g,\gamma ,\mathbf{d}}{]}^{vir}$, polynomial relations among GW and FJRW invariants of Fermat quintics are derived. In this paper, we prove a vanishing of a class of terms in $[({\mathcal{W}}_{g,\gamma ,\mathbf{d}}{)}^{{\mathbb{C}}^{\ast }}{]}^{vir}$. This vanishing verifies that in Witten's GLSM only $r$-spin invariants of insertions $2/5$ contribute to the phase transition between GW and FJRW invariants of Fermat quintics.

35pages

References in corpus (1)

• Mixed-Spin-P fields of Fermat quintic polynomials