2024/11/01 by J.L. Chkareuli, Chkareuli, J. L.
Earth and Planetary Sciences · Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #Geophysics and Gravity Measurements #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2411.11854
openalex publication_date 2024/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The perspective that gravity may govern the unification of all elementary forces calls for extending the gauge-gravity symmetry SL(2,C) to the broader local symmetry SL(2N,C), where N reflects the internal SU(N) subgroup. This extension yields a consistent hyperunification framework in which -- aside from the linear gravity Lagrangian, to which only tensor fields contribute -- the quadratic curvature sector is fully unified across all gauge submultiplets. Tetrad fields play a central role: once dynamical, their invertibility -- treated as a nonlinear sigma-model type length constraint -- naturally implies condensation and thereby triggers spontaneous breaking of SL(2N,C). As a result, while the full gauge multiplet contains vector, axial-vector, and tensor submultiplets, only the vector submultiplet remains in the observed spectrum; the axial-vector and tensor submultiplets acquire large masses at the symmetry-breaking scale. The effective symmetry reduces to SL(2,C)× SU(N), collecting together SL(2,C) gauge gravity and the SU(N) grand-unified sector. Since states in SL(2N,C) are also classified by spin magnitudes, many SU(N) GUT models -- such as standard SU(5)% -- appear ill-suited for fundamental spin-1/2 quarks and leptons. By contrast, applying SL(2N,C) to a composite framework with chiral preons in fundamental representations points to SL(16,C), with effective % SL(2,C)× SU(8) accommodating all three quark-lepton families, as a compelling candidate for hyperunification of all fundamental forces.