Abstract
We develop techniques, based on differential geometry, to compute holomorphic Yukawa couplings for heterotic line bundle models on Calabi-Yau manifolds defined as complete intersections in projective spaces. It is shown explicitly how these techniques relate to algebraic methods for computing holomorphic Yukawa couplings. We apply our methods to various examples and evaluate the holomorphic Yukawa couplings explicitly as functions of the complex structure moduli. It is shown that the rank of the Yukawa matrix can decrease at specific loci in complex structure moduli space. In particular, we compute the up Yukawa coupling and the singlet-Higgs-lepton trilinear coupling in the heterotic standard model described in arXiv:1404.2767
Highlights
String model building based on heterotic Calabi-Yau compactifications [1,2,3] has seen considerable progress over the past ten years [4]–[14] and large classes of models with the MSSM spectrum can be constructed using algorithmic approaches [15,16,17]
We develop techniques, based on differential geometry, to compute holomorphic Yukawa couplings for heterotic line bundle models on Calabi-Yau manifolds defined as complete intersections in projective spaces
We will attempt to make some progress in this direction and develop new methods, mainly based on differential geometry, to calculate holomorphic Yukawa couplings for heterotic line bundle models
Summary
String model building based on heterotic Calabi-Yau compactifications [1,2,3] has seen considerable progress over the past ten years [4]–[14] and large classes of models with the MSSM spectrum can be constructed using algorithmic approaches [15,16,17]. We will attempt to make some progress in this direction and develop new methods, mainly based on differential geometry, to calculate holomorphic Yukawa couplings for heterotic line bundle models. We would like to develop explicit methods based on differential geometry to compute the holomorphic Yukawa couplings for heterotic models with non-standard embedding. We will lay the ground by reviewing some of the basics, including the general structure of heterotic Yukawa couplings, heterotic line bundle models and complete intersection Calabi-Yau manifolds. Since our main focus will be on the tetra-quadric Calabi-Yau manifold we need to understand in some detail the differential geometry of P1 and its line bundles Appendix D proofs a crucial but somewhat technical property for bundlevalued harmonic forms on P1 which is the key to establishing the relation between the analytic and the algebraic calculation of Yukawa couplings
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