Lattice Gauge Theory with the 600-Cell: Freezing, Shadow Superposition, and a Persistent Mass Gap (INDYNA Research Note 38)

Abstract

The 120 icosians — the vertices of the 600-cell — form the largest finite subgroup of SU(2) and have been used as its lattice gauge group since Petcher and Weingarten. We reproduce the SU(2) behaviour of the plaquette with the 600-cell up to its freezing point, and show that superposing the golden shadow (the register's counter-rotation law: the point set joined with a copy rotated by 18°, then by 9°) moves the freezing transition systematically towards the continuum. The string tension from Creutz ratios is preserved at every stage and follows the SU(2) fall with the coupling. This is numerical evidence on a 4⁴ lattice, not a construction of continuum Yang–Mills theory and not a proof of the mass gap.