CFT Primary Operators

Conformal maps, operator dimensions, two-point functions on cylinder and plane
Scaling dim. Δ1.00
Spin s0
Central charge c0.50
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Conformal Field Theory: scale-invariant QFT with full conformal symmetry group. In 2D, the symmetry is infinite-dimensional (Virasoro algebra).
Primary operators O(z,z̄) with conformal weights (h,h̄) transform as O → (dw/dz)^h (dw̄/dz̄)^h̄ O under w(z). Scaling dimension Δ=h+h̄, spin s=h−h̄.
Cylinder↔Plane map: w = e^{2πz/L} maps the cylinder to the punctured plane. States on cylinder ↔ operators at origin.
Two-point function: ⟨O(z)O(0)⟩ = 1/|z|^{2Δ} — power law decay with exponent Δ.