Proton Decay, Yukawa Couplings and Underlying Gauge Symmetry in String Theory

TL;DR

This paper explores how string theory's gauge symmetry breaking can naturally suppress proton decay by assigning different origins to certain particles, with implications for unification models like E7 and E8.

Contribution

It proposes a novel mechanism where particles originate from different components of gauge symmetry breaking, constraining Yukawa couplings and proton decay operators in string-derived models.

Findings

E7 and E8 are minimal gauge groups compatible with Yukawa coupling generation.

The approach confirms the absence of dimension-4 proton decay operators in string models.

Gauge symmetry constraints influence effective field theory operators.

Abstract

In string theory, massless particles often originate from a symmetry breaking of a large gauge symmetry G to its subgroup H. The absence of dimension-4 proton decay in supersymmetric theories suggests that (\bar{D},L) are different from \bar{H}(\bar{\bf 5}) in their origins. In this article, we consider a possibility that they come from different irreducible components in $\mathfrak{g}/\mathfrak{h}$. Requiring that all the Yukawa coupling constants of quarks and leptons be generated from the super Yang--Mills interactions of G, we found in the context of Georgi--Glashow H=SU(5) unification that the minimal choice of G is E_7 and E_8 is the only alternative. This idea is systematically implemented in Heterotic String, M theory and F theory, confirming the absence of dimension 4 proton decay operators. Not only H=SU(5) but also G constrain operators of effective field theories, providing non-trivial information.