CFT Primary Operator Correlators

Two- and three-point functions fixed by conformal symmetry
2-Point Function
3-Point Function
Conformal Block
1.00 1.50
2.00 2.0
1.00 0.30
Ward Identities fix correlators:
⟨O₁(x₁)O₂(x₂)⟩ = C₁₂ / |x₁₂|^(2Δ) (requires Δ₁=Δ₂)
⟨O₁O₂O₃⟩ = C₁₂₃ / |x₁₂|^(Δ₁+Δ₂−Δ₃) |x₁₃|^(Δ₁+Δ₃−Δ₂) |x₂₃|^(Δ₂+Δ₃−Δ₁)
4-point functions: ⟨O₁O₂O₃O₄⟩ = f(u,v) × (kinematic prefactor) where u,v are conformal cross-ratios