Aspects of Flavour and Supersymmetry in F-theory GUTs

TL;DR

This paper investigates how supersymmetry constraints influence flavor structures in F-theory GUT models, deriving explicit wavefunction and Yukawa coupling solutions that result in a rank-one Yukawa matrix.

Contribution

It provides a detailed analysis linking topologically twisted theories to 8D super Yang-Mills and explicitly solves for wavefunctions and Yukawas considering metric and flux perturbations.

Findings

Yukawa matrix is rank-one with no subleading corrections

Holomorphy constrains Yukawa couplings and their scaling with _{GUT}

Explicit second-order solutions for wavefunctions and Yukawas

Abstract

We study the constraints of supersymmetry on flavour in recently proposed models of F-theory GUTs. We relate the topologically twisted theory to the canonical presentation of eight-dimensional super Yang-Mills and provide a dictionary between the two. We describe the constraints on Yukawa couplings implied by holomorphy of the superpotential in the effective 4-dimensional supergravity theory, including the scaling with \alpha_{GUT}. Taking D-terms into account we solve explicitly to second order for wavefunctions and Yukawas due to metric and flux perturbations and find a rank-one Yukawa matrix with no subleading corrections.