Non-Higgsable QCD and the standard model spectrum in F-theory

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) × 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) × SU(2) × 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) × 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.