Yukawa couplings in intersecting D-brane models

TL;DR

This paper calculates Yukawa couplings in intersecting D-brane models on toroidal compactifications, revealing their dependence on moduli and their mathematical interpretation via mirror symmetry and Fukaya categories.

Contribution

It provides explicit formulas for Yukawa couplings in intersecting D-brane models and extends methods to elliptically fibered Calabi-Yau manifolds, linking physics with advanced mathematics.

Findings

Yukawa couplings depend on Kahler and open string moduli, not on complex structure.

Couplings are expressed as products of Jacobi theta functions.

Mathematically, couplings relate to homological mirror symmetry and Fukaya categories.

Abstract

We compute the Yukawa couplings among chiral fields in toroidal Type II compactifications with wrapping D6-branes intersecting at angles. Those models can yield realistic standard model spectrum living at the intersections. The Yukawa couplings depend both on the Kahler and open string moduli but not on the complex structure. They arise from worldsheet instanton corrections and are found to be given by products of complex Jacobi theta functions with characteristics. The Yukawa couplings for a particular intersecting brane configuration yielding the chiral spectrum of the MSSM are computed as an example. We also show how our methods can be extended to compute Yukawa couplings on certain classes of elliptically fibered CY manifolds which are mirror to complex cones over del Pezzo surfaces. We find that the Yukawa couplings in intersecting D6-brane models have a mathematical interpretation in the context of homological mirror symmetry. In particular, the computation of such Yukawa couplings is related to the construction of Fukaya's category in a generic symplectic manifold.