Genus one stable quasimap invariants for projective complete intersections

TL;DR

This paper derives a new formula for genus one stable quasimap invariants of complete intersection Calabi-Yau manifolds in projective space, providing a novel proof of the mirror theorem for elliptic quasimap invariants.

Contribution

It introduces a new approach using infinitesimal marking points and explicit double J-function formulas to compute genus one invariants, offering a fresh proof of existing mirror symmetry results.

Findings

Derived a formula for genus one quasimap invariants

Provided a new proof of the mirror theorem for elliptic invariants

Extended techniques to complete intersection Calabi-Yau cases

Abstract

By using the infinitesimally marking point to break the loop in the localization calculation as Kim and Lho, and Zinger's explicit formulas for double $J$-functions, we obtain a formula for genus one stable quasimaps invariants when the target is a complete intersection Calabi-Yau in projective space, which gives a new proof of Kim and Lho's mirror theorem for elliptic quasimap invariants.