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Yang-Mills theories: Direct internal forces and emerging gravity
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 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 tetrad multiplets are treated as constrained dynamical fields selecting a neutral internal symmetry branch. This realizes the breaking , 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 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 -covariant matter sector that defines the unified gauge coupling. Finally, the matter sector points to a deeper elementarity of spinors, identified with preon constituents whose bound states form the observed quarks and leptons. Anomaly matching between preons and composites singles out . The chain then naturally yields three composite quark-lepton families, while filtering out extraneous heavy states.
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