BCT Letter 10: The Standard Model Gauge Group SU(3)xSU(2)_LxU(1)_Y from BCT Void Topology

The gauge group SU(3)C × SU(2)L × U(1)Y of the Standard Model is postulated, not derived: no principle within the Standard Model explains why these particular groups govern the fundamental interactions. Within the Body-Centred Tetragonal (BCT) Superfluid Lattice Model, the entire gauge structure emerges from the topology of the interstitial voids. SU(3)C arises from the three independent winding axes of vortex lines threading the tetrahedral voids, which have three pairs of opposite edges giving three colour charges. SU(2)L arises from the parity structure of the void sublattice: the tetrahedral void group Td distinguishes left-handed and right-handed vortex configurations through its improper rotation elements (S4), breaking parity maximally and coupling only to left-handed fermions. U(1)Y arises from the compact phase of the superfluid order parameter in the octahedral voids, with electric charge quantisation following from vortex winding number quantisation. The fractional quark charge Q = 1/3 follows from Chern–Simons quantisation on the tetrahedral void: the winding number of a vortex line around a tetrahedral void edge is quantised in units of 1/3 due to the three-fold topology. No gauge groups are assumed—they are consequences of how vortex lines can wrap around the voids of a BCT lattice.