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High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
Abstract:
We clarify and extend our earlier work (K.A.Meissner and H.Nicolai, Phys.
Rev. D91 (2015) 065029 and Phys. Rev. Lett. 121 (2018) 091601) 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 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)xU(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 x SU(2)_w x 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.
