SU(5/3) Superalgebra and Its Representations of Fundamental Particles
Chang-Ho Kim, Seung Kook Kim (Seonam U.), Young-Jai Park (Sogang, U.)
TL;DR
This paper explores the SU(5/3) superalgebra's representations to unify three generations of fundamental particles within a single mathematical framework, potentially advancing grand unified theories.
Contribution
It identifies a specific atypical irreducible representation of SU(5/3) that can encompass all known quarks and leptons, offering a novel unification approach.
Findings
All known quarks and leptons fit into one atypical irreducible representation.
The SU(5/3) superalgebra naturally includes an SU(5) subalgebra with additional SU(3) structure.
The study employs Kac-Dynkin weight techniques to analyze representations.
Abstract
We study the lowest dimensional typical and atypical representations of SU(5/3) superalgebra as a possible unified gauge theory having a natural SU(5) subalgebra with SU(3) extra structure, which will be used to accommodate three generations of fundamental particles. By using Kac-Dynkin weight techniques, we find that all known quarks and leptons can be really accommodated in one atypical irreducible representation of SU(5/3).
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