Standard Model Fermions and Infinite-Dimensional R-Symmetries

Abstract

Following up on our earlier work 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 3x16 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(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.