Fermion Wavefunctions in Magnetized branes: Theta identities and Yukawa couplings

TL;DR

This paper develops a comprehensive method to compute fermion wavefunctions and Yukawa couplings in magnetized brane models with oblique fluxes, using theta function identities, to aid phenomenological model building.

Contribution

It introduces explicit wavefunction solutions for general fluxes and mappings between different chiralities, enabling precise Yukawa coupling calculations in complex flux configurations.

Findings

Derived explicit fermion wavefunctions for arbitrary flux matrices.

Established identities for Riemann theta functions with matrix parameters.

Applied the method to mass generation in an SU(5) GUT model.

Abstract

Computation of Yukawa couplings, determining superpotentials as well as the K\"{a}hler metric, with oblique (non-commuting) fluxes in magnetized brane constructions is an interesting unresolved issue, in view of the importance of such fluxes for obtaining phenomenologically viable models. In order to perform this task, fermion (scalar) wavefunctions on toroidally compactified spaces are presented for general fluxes, parameterized by Hermitian matrices with eigenvalues of arbitrary signatures. We also give explicit mappings among fermion wavefunctions, of different internal chiralities on the tori, which interchange the role of the flux components with the complex structure of the torus. By evaluating the overlap integral of the wavefunctions, we give the expressions for Yukawa couplings among chiral multiplets arising from an arbitrary set of branes (or their orientifold images). The method is based on constructing certain mathematical identities for general Riemann theta functions with matrix valued modular parameter. We briefly discuss an application of the result, for the mass generation of non-chiral fermions, in the SU(5) GUT model presented by us in arXiv:0709.2799.