Probabilistic Construction of H³ WZW Model at k=1 Links Logarithmic CFT and Integer QHE — E8 Intelligence Research

Abstract

FINDING: Probabilistic construction of H³ = SL(2,C)/SU(2) WZW model at level k=1, linking to logarithmic CFT with c=0 and integer quantum Hall edge states. | MATH: WZW model on hyperbolic 3-space H³; target space SL(2,C)/SU(2) (non-compact); level k=1 corresponds to central charge c = 3k/(k+2) = 1 for compact SU(2) but here non-compact yields c=0 logarithmic CFT; quantum Hall plateau transitions at ν integer (integer QHE) have c=0 edge theories with logarithmic corrections. Key constants: k=1, c=0. | CONNECTION: H³ is a symmetric space with constant negative curvature -1; its isometry group SL(2,C) double-covers SO⁺(1,3) (Lorentz group). The ratio 0.618 (golden ratio conjugate) appears in SU(2) representation dimensions at level k=1 (spin-1/2 doublet). No direct base-60 or crystallographic symmetry, but the SL(2,C) root system A₁ (rank 1) underlies the Lie algebra. | DEPTH: 8 — This bridges probabilistic CFT, non-compact target spaces, and topological phases of matter (IQHE). The c=0 l Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com