2007/03/31 by Volker Braun, Burt A Ovrut, Maximilian Kreuzer +2 · 3 citations
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Geometry and complex manifolds #hep-th
paper · pdf · doi:10.1088/1126-6708/2007/10/022
published as JHEP0710:022,2007 · 67 pages, LaTeX. v2: reference added
arxiv created 2007/06/22 · openalex publication_date 2007/10/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
As a first step towards studying vector bundle moduli in realistic heterotic compactifications, we identify all holomorphic rational curves in a Calabi-Yau threefold X with Z3 x Z3 Wilson lines. Computing the homology, we find that H2(X,Z)=Z3+Z3+Z3. The torsion curves complicate our analysis, and we develop techniques to distinguish the torsion part of curve classes and to deal with the non-toric threefold X. In this paper, we use direct A-model computations to find the instanton numbers in each integral homology class, including torsion. One interesting result is that there are homology classes that contain only a single instanton, ensuring that there cannot be any unwanted cancellation in the non-perturbative superpotential.