Operator Product Expansion

Short-distance singularities and the algebraic structure of local operators in CFT

Parameters

OPE Structure

Theory

O₁(x)O₂(0) = Σ_k C₁₂ᵏ |x|^{Δk-Δ1-Δ2} Oₖ(0)
The OPE is an exact operator relation in CFT (not just a short-distance approximation). The sum runs over all primaries and their descendants.
C₁₂ᵏ: structure constants = CFT data
The singular terms are fixed by conformal invariance; the OPE coefficients C₁₂ᵏ are the dynamical data of the CFT. Together with the spectrum {Δₖ}, they fully determine all correlators.