Standard Model Fermions and Infinite-Dimensional R Symmetries

Abstract

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-12 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(E10) of the conjectured maximal duality symmetry E10. As a by-product, it predicts fractionally charged and possibly strongly interacting massive gravitinos. It also indicates how E10 and K(E10) can supersede supersymmetry as a guiding principle for unification.