$E_6$ Yukawa couplings in F-theory as D-brane instanton effects

TL;DR

This paper investigates the origin of $E_6$ Yukawa couplings in F-theory models, demonstrating they arise from D-brane instanton effects in a weak coupling limit and exploring their behavior across different string theory regimes.

Contribution

It explicitly shows that $E_6$ Yukawa couplings in F-theory are generated by non-perturbative D-brane instantons, connecting weak and strong coupling descriptions.

Findings

$E_6$ Yukawa couplings are from D1-brane instantons in a weak coupling limit.

The weak coupling limit involves a non-resolvable orientifold of the conifold.

M-theory provides an interpolation between weak and strong coupling perspectives.

Abstract

In a weak coupling limit the neighborhood of $E_6$ Yukawa points in $SU(5)$ GUT F-theory models is described by a non-resolvable orientifold of the conifold. We explicitly show, first directly in IIB and then via a mirror symmetry argument, that in this limit the $E_6$ Yukawa coupling is better described as coming from the non-perturbative contribution of a euclidean D1-brane wrapping the non-resolvable cycle. We also discuss how the M-theory description interpolates between the weak and strong coupling viewpoints.