Wavefunctions and the Point of E8 in F-theory

TL;DR

This paper investigates the structure of operators in F-theory GUTs with E8 symmetry enhancement, focusing on wavefunction overlaps and flux constraints to understand Yukawa and proton decay operators.

Contribution

It develops a framework for calculating wavefunctions and overlaps at E8 points in F-theory GUTs, advancing the understanding of local operator structures.

Findings

Wavefunctions and overlaps are computed around E8 points.

Flux constraints on local wavefunctions are established.

Example operators like Yukawa couplings are explicitly calculated.

Abstract

In F-theory GUTs interactions between fields are typically localised at points of enhanced symmetry in the internal dimensions implying that the coefficient of the associated operator can be studied using a local wavefunctions overlap calculation. Some F-theory SU(5) GUT theories may exhibit a maximum symmetry enhancement at a point to E8, and in this case all the operators of the theory can be associated to the same point. We take initial steps towards the study of operators in such theories. We calculate wavefunctions and their overlaps around a general point of enhancement and establish constraints on the local form of the fluxes. We then apply the general results to a simple model at a point of E8 enhancement and calculate some example operators such as Yukawa couplings and dimension-five couplings that can lead to proton decay.