Worldsheet Instantons, Torsion Curves, and Non-Perturbative Superpotentials

Details Worldsheet Instantons, Torsion Curves, and Non-Perturbative Superpotentials Worldsheet Instantons, Torsion Curves, and Non-Perturbative Superpotentials

2007-03-14

arxiv.org/abs/hep-th/0703134v1

Phys.Lett.B649:334-341,2007

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, LaTeX

Scientific paper

10.1016/j.physletb.2007.03.066

As a first step towards computing instanton-generated superpotentials in heterotic standard model vacua, we determine the Gromov-Witten invariants for a Calabi-Yau threefold with fundamental group pi_1(X)=Z_3 x Z_3. We find that the curves fall into homology classes in H_2(X,Z)=Z^3+(Z_3+Z_3). The unexpected appearance of the finite torsion subgroup in the homology group complicates our analysis. However, we succeed in computing the complete genus-0 prepotential. Expanding it as a power series, the number of instantons in any integral homology class can be read off. This is the first explicit calculation of the Gromov-Witten invariants of homology classes with torsion. We find that some curve classes contain only a single instanton. This ensures that the contribution to the superpotential from each such instanton cannot cancel.

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