Minimal Models in CFT: Discrete Central Charges and the Ising Case — E8 Intelligence Research

FINDING: Minimal models in CFT are characterized by a discrete set of allowed central charges and conformal weights, with the simplest nontrivial case being central charge c = 1/2 (the Ising model), whose operator product expansions (OPEs) close on a finite set of primary fields. MATH: - Central charge: c = 1/2 (Ising model). - Kac determinant vanishes at null states; for minimal models, c = 1 − 6(p−q)²/(pq), with p,q coprime integers. For c = 1/2: (p,q) = (4,3) or (3,4). - Conformal weights: h = 0, 1/16, 1/2 (identity, spin, energy fields). - OPE structure: φ(1/16) × φ(1/16) = [1] + [ε(1/2)]; φ(1/2) × φ(1/2) = [1]; φ(1/16) × φ(1/2) = φ(1/16). - Fusion rules: Z₂ grading (even/odd sectors) — a finite group structure. CONNECTION: - The ratio 1/16 = 0.0625, and 1/2 = 0.5 — but more striking: the fusion rules mirror the multiplication table of the group Z₂, and the central charge 1/2 is exactly half of the free boson c=1. - The minimal model series includes c = 1/2, 7/1 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com