2007/03/14 by Volker Braun, Maximilian Kreuzer, Burt A. Ovrut +1 · 4 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Geometry and complex manifolds #Quantum Chromodynamics and Particle Interactions #hep-th
paper · pdf · doi:10.1016/j.physletb.2007.03.066
published as Phys.Lett.B649:334-341,2007 · 14 pages, LaTeX
arxiv created 2007/03/14 · openalex publication_date 2007/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
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 π1(X)=Z3×Z3. We find that the curves fall into homology classes in H2(X,Z)=Z3⊕(Z3⊕Z3). 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.