Worldsheet Instantons and Torsion Curves, Part A: Direct Computation

Abstract

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 Z_3 x Z_3 Wilson lines. Computing the homology, we find that H_2(X,Z)=Z^3+Z_3+Z_3. 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.

67 pages, LaTeX. v2: reference added

References in corpus (5)

• The Exact MSSM Spectrum from String Theory
• Yukawa Couplings in Heterotic Standard Models
• Stabilizing Moduli with a Positive Cosmological Constant in Heterotic M-Theory
• Worldsheet Instantons, Torsion Curves, and Non-Perturbative Superpotentials
• Stability of the Minimal Heterotic Standard Model Bundle

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• Line Bundle Hidden Sectors for Strongly Coupled Heterotic Standard Models
• Type II String Theory on Calabi-Yau Manifolds with Torsion and Non-Abelian Discrete Gauge Symmetries
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• Bagger-Witten line bundles on moduli spaces of elliptic curves
• Three Generations on the Quintic Quotient
• Higgs Multiplets in Heterotic GUT Models
• Constraints on heterotic M-theory from s-cobordism
• Noncommutative resolutions and CICY quotients from a non-abelian GLSM