Conformal Field Theory — Operator Product Expansion

In a 2D CFT, primary operators transform as O(z)→(dw/dz)^hO(w). The OPE encodes all local data: T(z)O(w) ~ hO(w)/(z−w)² + ∂O(w)/(z−w). Visualize conformal transformations of the complex plane.

T(z)T(w) ~ c/2(z−w)⁴ + 2T(w)/(z−w)² + ∂T(w)/(z−w) | T(z)O(w) ~ hO(w)/(z−w)² + ∂O(w)/(z−w)

Transform

Grid density8

Dim h1.0

Animateon