Standard model fermions and $N=8$ supergravity

In a scheme originally proposed by Gell-Mann, and subsequently shown to be realized at the $\mathrm{SU}(3)\times \mathrm{U}(1)$ stationary point of maximal gauged SO(8) supergravity by Warner and one of the present authors, the 48 spin-$\frac{1}{2}$ fermions of the theory remaining after the removal of eight Goldstinos can be identified with the 48 quarks and leptons (including right-chiral neutrinos) of the Standard model, provided one identifies the residual SU(3) with the diagonal subgroup of the color group $\mathrm{SU}(3{)}_c$ and a family symmetry $\mathrm{SU}(3{)}_f$. However, there remained a systematic mismatch in the electric charges by a spurion charge of $\pm \frac{1}{6}$. We here identify the “missing” U(1) that rectifies this mismatch, and that takes a surprisingly simple, though unexpected form.