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SL(2N,C) Yang-Mills theories: Direct internal forces and emerging gravity

J. L. Chkareuli

Phys. Rev. D 114, 055038 – Published 21 September, 2026

DOI: https://doi.org/10.1103/4v84-pz6v

Abstract

A four-dimensional gauge-gravity unification based on local SL(2N,C) symmetry is developed in a universal Yang-Mills-type setting, which, however, appears dynamically consistent only in the symmetry-broken phase. In the exact symmetry limit, the theory may only be formulated in a premetric framework, where the accompanying tetrad multiplets, though promoted to dynamical fields, do not yet satisfy the conventional invertibility conditions. An ordinary Einstein-Cartan spacetime geometry emerges only in the broken postsoldering phase, in which the SL(2N,C) tetrad multiplets are treated as constrained dynamical fields selecting a neutral internal symmetry branch. This realizes the breaking SL(2N,C)→SL(2,C)×SU(N), thereby lifting all noncompact internal directions, while the surviving neutral tetrad is, as usual, associated with the gravitational field. A special ghost-free curvature-squared Lagrangian provides a consistent quadratic sector for the spin connection, propagating only admissible connection modes: the massless SU(N) vector fields together with massive axial-vector and pseudoscalar multiplets. The Einstein-Cartan linear curvature term is argued to arise radiatively from fermion loops, thereby relating the gravitational scale to the same SL(2N,C)-covariant matter sector that defines the unified gauge coupling. Finally, the matter sector points to a deeper elementarity of SL(2N,C) spinors, identified with preon constituents whose bound states form the observed quarks and leptons. Anomaly matching between preons and composites singles out N=8. The chain SL(16,C)→SL(2,C)×SU(8) then naturally yields three composite quark-lepton families, while filtering out extraneous heavy states.

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