Mixed-Spin-P fields of Fermat quintic polynomials

TL;DR

This paper introduces Mixed-Spin-P fields and constructs their moduli spaces and virtual cycles as part of developing algorithms to compute Gromov-Witten invariants of quintic Calabi-Yau threefolds.

Contribution

It defines Mixed-Spin-P fields, constructs their moduli spaces, and develops foundational tools for calculating Gromov-Witten invariants.

Findings

Construction of moduli spaces for Mixed-Spin-P fields

Development of virtual cycles for these moduli spaces

Foundation for an algorithm to evaluate Gromov-Witten invariants

Abstract

This is the first part of the project toward an effective algorithm to evaluate all genus Gromov-Witten invariants of quintic Calabi-Yau threefolds. In this paper, we introduce the notion of Mixed-Spin-P fields, construct their moduli spaces, and construct the virtual cycles of these moduli spaces.