Worldsheet Instantons and Torsion Curves

TL;DR

This paper computes genus-0 Gromov-Witten invariants for a non-toric Calabi-Yau threefold with torsion homology classes, revealing unique instanton contributions relevant to heterotic string models.

Contribution

It provides the first explicit calculation of Gromov-Witten invariants for homology classes with torsion on a non-toric Calabi-Yau threefold, advancing understanding of worldsheet instantons.

Findings

Homology classes are Z^3 + Z_3 + Z_3.

Some curve classes contain only a single instanton.

Beasley-Witten cancellation does not occur on this manifold.

Abstract

We study aspects of worldsheet instantons relevant to a heterotic standard model. The non-simply connected Calabi-Yau threefold used admits Z_3 x Z_3 Wilson lines, and a more detailed investigation shows that the homology classes of curves are H_2(X,Z)=Z^3+Z_3+Z_3. We compute the genus-0 prepotential, this is the first explicit calculation of the Gromov-Witten invariants of homology classes with torsion (finite subgroups). In particular, some curve classes contain only a single instanton. This ensures that the Beasley-Witten cancellation of instanton contributions cannot happen on this (non-toric) Calabi-Yau threefold.