General linear matrix model, Minkowski spacetime and the Standard Model

Abstract

The Hermitian matrix model with general linear symmetry is argued to decouple into a finite unitary matrix model that contains metastable multidimensional lattice configurations and a fermion determinant. The simplest metastable state is a Hermitian Weyl kinetic operator of either handedness on a 3+1 D lattice with general nonlocal interactions. The Hermiticity produces 16 effective Weyl fermions by species doubling, 8 left- and 8 right-handed. These are identified with a Standard Model generation. Only local non-anomalous gauge fields within the soup of general fluctuations can survive at long distances, and the degrees of freedom for gauge field subgroups of $U(8)_L X U(8)_R$ are present. Standard Model gauge symmetries associate with particular species symmetries, for example change of QCD color associates with permutation of doubling status amongst space directions. Vierbein gravity is probably also generated. While fundamental Higgs fields are not possible, low fermion current masses can arise from chiral symmetry breaking solutions of the fermion self-energy Schwinger-Dyson equations, generating W mass and composite Higgs states, similar to a scheme proposed by Gribov. Specific higher dimensional lattices with larger spinors are potentially stable but produce non-Riemannian spaces without conserved quadratic distances. However if the extra dimensions are compactified, the Minowski space persists at low energy accompanied by SM generations, potentially doubled further by duplicate zero modes in the compact directions and potentially containing dark matter. The model is conjectured to have an origin in infinite dimensional conformal invariance and the concept of Bare Particulars.