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

TL;DR

This paper proposes a unification of gauge and gravity theories using an $SL(2N,C)$ gauge framework, leading to spontaneous symmetry breaking, mass generation for gauge fields, and a potential preon model explaining quark and lepton families.

Contribution

It introduces a novel $SL(2N,C)$ gauge theory with dynamical tetrads, spontaneous symmetry breaking, and a preon-based matter sector explaining fermion families.

Findings

Spontaneous symmetry breaking from $SL(2N,C)$ to $SL(2,C)\times SU(N)$.

Massless graviton and gauge fields emerge below the breaking scale.

Three fermion families arise naturally from anomaly matching.

Abstract

We develop a four-dimensional gauge-gravity unification based on the $% SL(2N,C)$ 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, $SL(2N,C)\rightarrow SL(2,C)\times SU(N)$, 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 $SL(16,C)\rightarrow SL(2,C)\times SU(8)$ then naturally yields three composite quark--lepton families, while filtering out extraneous heavy states.