Mean field theory is a generic name for conformal field theories that are built from generalized free fields. For example, a mean field theory can be built from one scalar primary field ϕ ϕ . Then this theory contains ϕ ϕ , its descendant fields, and the fields that appear in the OPE ϕ ϕ ϕ ϕ . The primary fields that appear in ϕ ϕ ϕ ϕ can be determined by decomposing the four-point function ⟨ ⟨ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ⟩ ⟩ in conformal blocks: their conformal dimensions belong to 2 Δ Δ + 2 N : in mean field theory, the conformal dimension is conserved modulo integers.