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Left-Right Symmetric Fermions and Sterile Neutrinos from Complex Split Biquaternions and Bioctonions

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Abstract

In this article we investigate the application of complex split biquaternions and bioctonions to the standard model. We show that the Clifford algebras Cl(3) and Cl(7) can be used for making left-right symmetric fermions. Hence we incorporate right-handed neutrinos in the division algebras-based approach to the standard model. The right-handed neutrinos, or sterile neutrinos, are a potential dark-matter candidate. Using the division algebra approach, we discuss the left-right symmetric fermions and their phenomenology. We describe the gauge groups associated with the left-right symmetric model and prospects for unification through division algebras. We briefly discuss the possibility of obtaining three generations of fermions and charge/mass ratios through the exceptional Jordan algebra \(J_3(O)\) and the exceptional groups \(F_4\) and \(E_6\).

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Acknowledgements

It is a pleasure to thank Vivan Bhatt, Priyank Kaushik, Rajrupa Mondal, and Robert Wilson for several helpful discussions. The authors are very thankful to the referees for their feedback and for playing a crucial role in improving this manuscript.

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Authors and Affiliations

  1. Indian Institute of Technology, Kanpur, 208016, India

    Vatsalya Vaibhav

  2. Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400005, India

    Tejinder P. Singh

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  1. Vatsalya Vaibhav
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Correspondence to Tejinder P. Singh.

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Vaibhav, V., Singh, T.P. Left-Right Symmetric Fermions and Sterile Neutrinos from Complex Split Biquaternions and Bioctonions. Adv. Appl. Clifford Algebras 33, 32 (2023). https://doi.org/10.1007/s00006-023-01278-8

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