Non-Higgsable QCD and the Standard Model Spectrum in F-theory

TL;DR

This paper explores how certain geometric structures in F-theory naturally produce parts of the Standard Model, like QCD, without requiring symmetry breaking, offering insights into the origin of light particles and forces.

Contribution

It identifies three geometric scenarios in F-theory that realize non-Higgsable SU(3) and SU(2) sectors consistent with the Standard Model, including anomaly cancellation and matter localization.

Findings

Three distinct F-theory realizations of the Standard Model gauge group.

Identification of geometries with non-Higgsable SU(3) and SU(3)×SU(2) sectors.

A natural mechanism for unbroken QCD and light particles in string compactifications.

Abstract

Many four-dimensional supersymmetric compactifications of F-theory contain gauge groups that cannot be spontaneously broken through geometric deformations. These "non-Higgsable clusters" include realizations of $SU(3)$, $SU(2)$, and $SU(3) \times SU(2)$, but no $SU(n)$ gauge groups or factors with $n> 3$. We study possible realizations of the standard model in F-theory that utilize non-Higgsable clusters containing $SU(3)$ factors and show that there are three distinct possibilities. In one, fields with the non-abelian gauge charges of the standard model matter fields are localized at a single locus where non-perturbative $SU(3)$ and $SU(2)$ seven-branes intersect; cancellation of gauge anomalies implies that the simplest four-dimensional chiral $SU(3)\times SU(2)\times U(1)$ model that may arise in this context exhibits standard model families. We identify specific geometries that realize non-Higgsable $SU(3)$ and $SU(3) \times SU(2)$ sectors. This kind of scenario provides a natural mechanism that could explain the existence of an unbroken QCD sector, or more generally the appearance of light particles and symmetries at low energy scales.