2023/10/18 by J.L. Chkareuli, Chkareuli, J. L.
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies
paper · pdf · doi:10.48550/arxiv.2310.11847
openalex publication_date 2023/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The local SL(2N,C) symmetry is shown to provide, when appropriately constrained, a viable framework for a consistent unification of the known elementary forces, including gravity. Such a covariant constraint implies that an actual gauge field multiplet in the SL(2N,C) theory is ultimately determined by the associated tetrad fields which not only specify the geometric features of spacetime but also govern which local internal symmetries are permissible within it. As a consequence, upon the covariant removal of all "redundant" gauge field components, the entire theory only exhibits the effective SL(2,C)× SU(N) symmetry, comprising SL(2,C) gauge gravity on one hand and SU(N) grand unified theory on the other. Given that all states involved in the SL(2N,C) theories are additionally classified according to their spin values, many potential SU(N) GUTs, including the conventional SU(5) theory, appear to be irrelevant for standard spin 1/2 quarks and leptons. Meanwhile, applying the SL(2N,C) symmetry to the model of composite quarks and leptons with constituent chiral preons in its fundamental representations reveals, under certain natural conditions, that among all accompanying SU(N)L× SU(N)R chiral symmetries of preons and their composites only the SU(8)L× SU(8)R meets the anomaly matching condition ensuring masslessness of these composites at large distances. This, in turn, identifies SL(16,C) with the effective SL(2,C)× SU(8) symmetry, accommodating all three families of composite quarks and leptons, as the most likely candidate for hyperunification of the existing elementary forces.