Standard Model Fermions and Infinite-Dimensional R Symmetries.

Area of Science:

• Theoretical physics
• High-energy physics
• Quantum gravity

Background:

• N=8 supergravity possesses 48 spin-1/2 fermions.
• Previous work amended the Gell-Mann scheme to link these fermions to standard model quarks and leptons.
• Complete breaking of N=8 supersymmetry necessitates further generalization.

Purpose of the Study:

• To generalize the fermion identification scheme to include full Standard Model gauge and family symmetries.
• To explore the implications of embedding N=8 supergravity's R symmetry into the E10 symmetry group.
• To investigate E10 and its maximal compact subgroup K(E10) as a potential guiding principle for unification.

Main Methods:

• Generalization of a previously proposed scheme for fermion identification.
• Embedding the SU(8) R symmetry of N=8 supergravity into K(E10), the maximal compact subgroup of E10.
• Analysis of the resulting particle content and symmetry structure.

Main Results:

• The construction is generalized to accommodate SU(3)c×SU(2)w×U(1)Y and an additional family symmetry SU(3)f.
• The proposal relies on embedding SU(8) into K(E10).
• Fractionally charged and potentially strongly interacting massive gravitinos are predicted.

Conclusions:

• The generalized construction provides a framework for unifying Standard Model particles within N=8 supergravity.
• The embedding into E10 suggests a new paradigm for unification, potentially superseding supersymmetry.
• The predicted massive gravitinos offer testable consequences for future theories.