Invariant Homology on Standard Model Manifolds

Abstract

Torus-fibered Calabi-Yau threefolds Z, with base dP_9 and fundamental group pi_1(Z)=Z_2 X Z_2, are reviewed. It is shown that Z=X/(Z_2 X Z_2), where X=B X_{P_1} B' are elliptically fibered Calabi-Yau threefolds that admit a freely acting Z_2 X Z_2 automorphism group. B and B' are rational elliptic surfaces, each with a Z_2 X Z_2 group of automorphisms. It is shown that the Z_2 X Z_2 invariant classes of curves of each surface have four generators which produce, via the fiber product, seven Z_2 X Z_2 invariant generators in H_4(X,Z). All invariant homology classes are computed explicitly. These descend to produce a rank seven homology group H_4(Z,Z) on Z. The existence of these homology classes on Z is essential to the construction of anomaly free, three family standard-like models with suppressed nucleon decay in both weakly and strongly coupled heterotic superstring theory.

arXiv comment57 pages, 13 figures

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• Vacuum Stability in Heterotic M-Theory
• Calabi-Yau Metrics for Quotients and Complete Intersections
• The Spectra of Heterotic Standard Model Vacua
• Yukawa Couplings in Heterotic Standard Models
• On Classifying the Divisor Involutions in Calabi-Yau Threefolds
• Elliptic Calabi-Yau Threefolds with Z_3 x Z_3 Wilson Lines
• Towards Realizing Dynamical SUSY Breaking in Heterotic Model Building
• Stability of the Minimal Heterotic Standard Model Bundle
• Worldsheet Instantons and Torsion Curves, Part A: Direct Computation
• Moduli Dependent mu-Terms in a Heterotic Standard Model
• Heterotic Standard Model Moduli
• The Moduli of Reducible Vector Bundles
• Instanton Moduli in String Theory
• Moduli restriction and Chiral Matter in Heterotic String Compactifications
• Higgs Multiplets in Heterotic GUT Models