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 x 16 quarks and leptons of the standard model, we further generalize the construction to account for the full SU(3)(c) x SU(2)(w) x 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.