SL(2N,C) Hyperunification: Dynamical Tetrads, Induced Gravity, and Composite Families
Authors
J. L. Chkareuli
Abstract
A four-dimensional gauge--gravity unification based on the local $SL(2N,\mathbb{C})$ symmetry is developed in a universal Yang--Mills-type setting. The accompanying tetrads are promoted to dynamical fields, and their invertibility condition is interpreted as a nonlinear sigma-model-type length constraint. This triggers tetrad condensation and spontaneously breaks $SL(2N,\mathbb{C})$ down to $SL(2,\mathbb{C})\times SU(N)$, effectively filtering out unobserved non-compact directions. A special ghost-free curvature-squared Lagrangian provides a consistent quadratic sector for all gauge fields involved, while an Einstein--Cartan linear-curvature term is shown to arise radiatively from fermion loops. The matter sector points to a deeper elementarity of $SL(2N,\mathbb{C})$ 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 $SL(16,\mathbb{C})$, accommodating precisely three composite quark--lepton families. The theory thus links non-compact unification, induced gravity, and fermion family structure within a single framework.
