Standard Model Fermions and Infinite-Dimensional R Symmetries

Following up on our earlier work [K. A. Meissner and H. Nicolai, Phys. Rev. D 91, 065029 (2015)] where we showed how to amend a scheme originally proposed by M. Gell-Mann to identify the 48 spin-1/2 fermions of N=8 supergravity that remain after complete breaking of N=8 supersymmetry with the 3×16 quarks and leptons of the standard model, we further generalize the construction to account for the full SU(3)_{c}×SU(2)_{w}×U(1)_{Y} assignments, with an additional family symmetry SU(3)_{f}. Our proposal relies in an essential way on embedding the SU(8) R symmetry of N=8 supergravity into the (infinite-dimensional) "maximal compact" subgroup K(E_{10}) of the conjectured maximal duality symmetry E_{10}. As a by-product, it predicts fractionally charged and possibly strongly interacting massive gravitinos. It also indicates how E_{10} and K(E_{10}) can supersede supersymmetry as a guiding principle for unification.