A fourth generation of standard model fermions is usually considered unlikely due to constraints from direct searches, electroweak precision measurements, and perturbative unitarity. We show that fermion mass textures consistent with all constraints may be obtained naturally in a model with four generations constructed from intersecting $D6$-branes on a $T^6/({\mathbb{Z}}_2\times {\mathbb{Z}}_2)$ orientifold. The Yukawa matrices of the model are rank 2, so that only the third- and fourth-generation fermions obtain masses at the trilinear level. The first two generations obtain masses via higher-order couplings and are therefore naturally lighter. In addition, we find that the third and fourth generations automatically split in mass, but do not mix at leading order. Furthermore, the standard model gauge couplings automatically unify at the string scale, and all the hidden-sector gauge groups become confining in the range ${10}^{13}–{10}^{16}\mathrm{GeV}$, so that the model becomes effectively a four-generation minimal supersymmetric standard model at low energies.

• Received 28 April 2011

DOI:https://doi.org/10.1103/PhysRevD.84.105015