Beyond the standard model with six-dimensional spinors

David Chester; Michael Rios; Alessio Marrani

doi:10.3390/particles6010008

paper

Beyond the standard model with six-dimensional spinors

arXiv:2002.02391 · doi:10.3390/particles6010008

Abstract

6D spinors with $S p in (3, 3)$ symmetry are utilized to efficiently encode three generations of matter. $E_{8 (- 24)}$ is shown to contain physically relevant subgroups with representations for GUT groups, spacetime symmetries, three generations of the standard model fermions, and Higgs bosons. Pati-Salam, $S U (5)$ , and $S p in (10)$ grand unified theories are found when a single generation is isolated. For spacetime symmetries, $S p in (4, 2)$ may be used for conformal symmetry, $A d S_{5} \to d S_{4}$ , or simply broken to $S p in (3, 1)$ of Minkowski space. Another class of representations finds $S p in (2, 2)$ and can give $A d S_{3}$ with various GUTs. An action for three generations of fermions in the Majorana-Weyl spinor $128$ of $S p in (4, 12)$ is found with $S p in (3)$ flavor symmetry inside $E_{8 (- 24)}$ . The $128$ of $S p in (4, 12)$ can be regarded as the tangent space to a particular pseudo-Riemannian form of the octo-octonionic Rosenfeld projective plane $E_{8 (- 24)} / S p in (4, 12) = (O_{s} \times O) P^{2}$ .

28 pages with references, 1 figure; v3: Abstract changed, various updates based on feedback from referees, addition of Lagrangian for 3 generations

Beyond the standard model with six-dimensional spinors

Abstract

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