MERLIN SCIENCE — Weyl Group D6: Hexagonal Symmetry Unifying Lattice QCD and SU(3) — E8 Intelligence Research

Here is the narration for the MERLIN SCIENCE video. --- The finding is this: Lattice QCD and the representation theory of SU(3) converge on a single discrete symmetry—the Weyl group D6, the hexagonal root system. This is the rotational structure governing both quark-gluon dynamics and the construction of baryon operators on the lattice. For context. You work with SU(3) daily. It has eight generators, the Gell-Mann matrices, and rank two. That rank two is the key. The root system of SU(3) is A2, which is isomorphic to D2, and its six nonzero roots form a perfect regular hexagon. The Weyl group of A2 is the dihedral group D6, of order twelve. So the abstract color symmetry is hexagonally structured from the start. Now, the mechanism. On a hypercubic spacetime lattice, you break continuous rotational symmetry down to the cubic group, twenty-four elements. But the internal color symmetry does not break. The Cartan subalgebra remains two-dimensional, and the six roots—plus or minus one Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com