SL(2N,C) Yang-Mills Theories: Direct Internal Forces and Emerging Gravity

We develop a four-dimensional gauge-gravity unification based on the $$ gauge theory taken in a universal Yang–Mills type setting. The accompanying tetrads are promoted to dynamical fields whose length, when projected onto the background Minkowskian spacetime, is restricted by a nonlinear sigma-model type constraint. This triggers tetrad condensation and spontaneous symmetry breaking, $SL(2N,C)\to SL(2,C)\times SU(N)$, lifting all noncompact directions. A special ghost-free curvature-squared Lagrangian provides a consistent quadratic sector, while an Einstein–Cartan linear curvature term is induced radiatively from fermion loops. Below the breaking scale, only a neutral tetrad associated with graviton and $SU(N)$ vector fields remain massless, whereas axial-vector and tensor fields of the entire gauge multiplet acquire heavy masses. The matter sector clearly points to a deeper elementarity of $SL(2N,C)$ spinors, which can be 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 $SL(16,C)\to SL(2,C)\times SU(8)$ then naturally yields three composite quark–lepton families, while filtering out extraneous heavy states.