Standard model symmetries and K(E10)

A bstract We clarify and extend our earlier work 1, 2 where it was shown how to amend a scheme originally proposed by M. Gell-Mann to identify the three families of quarks and leptons of the Standard Model with the 48 spin- 12 1 2 fermions of N = 8 supergravity that remain after absorption of eight Goldstinos, a scheme that in its original form is dynamically realized at the SU (3) × U (1) stationary point of gauged N = 8 supergravity. We explain how to deform and enlarge this symmetry at the kinematical level to the full Standard Model symmetry group SU (3) c × SU (2) w × U (1) Y, with the correct charge and chiral assignments for all fermions. The framework also leaves room for an extra U (1) B−L symmetry. This symmetry enhancement is achieved by embedding the Standard Model symmetries into (a quotient group of) K (E 10), the ‘maximal compact subgroup’ of the maximal rank hyperbolic Kac-Moody symmetry E 10, and an infinite prolongation of the SU (8) R -symmetry of N = 8 supergravity. This scheme, which is also supposed to encompass quantum gravity, cannot be realized within the framework of space-time based (quantum) field theory, but requires space-time and related geometrical concepts to be ‘emergent’. We critically review the main hypotheses underlying this construction.