Worldsheet Instantons, Torsion Curves, and Non-Perturbative Superpotentials
摘要
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.
引用
@article{arxiv.hep-th/0703134,
title = {Worldsheet Instantons, Torsion Curves, and Non-Perturbative Superpotentials},
author = {Volker Braun and Maximilian Kreuzer and Burt A. Ovrut and Emanuel Scheidegger},
journal= {arXiv preprint arXiv:hep-th/0703134},
year = {2009}
}
备注
14 pages, LaTeX