Exceptional Unification of Families and Forces

Abstract: This work considers the remarkable suggestion that the three families of quarks and leptons may be unified, together with the Higgs and gauge fields of the Standard Model (SM), into a single "particle", namely the $\textbf{248}$ vector superfield of a ten-dimensional $E_8$ super Yang Mills (SYM) theory. Towards a realistic model along these lines, a class of orbifoldings based on $T^6/(\mathbb{Z}_N\times \mathbb{Z}_M)$ are proposed and explored, that can in principle break $E_8$ SYM down to the minimal supersymmetric standard model (MSSM), embedded in a larger group such as $E_6$, $SO(10)$ or $SU(5)$, together with other gauge group factors which can be broken by Wilson lines. A realistic model based on $T^6/(\mathbb{Z}_6\times \mathbb{Z}_2)$ is presented. The orbifold breaks $E_8$ SYM down to a Pati-Salam gauge group in 4d, together with other gauge groups, which are further broken to the SM by Wilson lines in the right-handed sneutrino directions, yielding proto-realistic fermion mass matrices, and experimental signals associated with a low Pati-Salam gauge group breaking scale.