Conformal Field Theory Correlators

Scale invariance constrains all correlation functions
⟨O(r₁) O(r₂)⟩ = C / |r₁ - r₂|^{2Δ}
Scaling dim Δ 0.50
Operator 1 x
Operator 2 x
Num operators 3
In Conformal Field Theory, scale and conformal invariance fix the form of all two-point functions exactly. The scaling dimension Δ (or conformal weight) is the only free parameter — it determines how correlations decay with distance. At critical points (like the 2D Ising model, Δ=1/8 for spin), the system is scale-free and described by a CFT. Three-point functions are also fixed up to a single OPE coefficient C₁₂₃.