(The identity field is the field whose insertion into correlation functions does not modify them, i.e. ⟨ I ( x ) ⋯ ⋯ ⟩ = ⟨ ⋯ ⋯ ⟩ .) The name comes from the fact that if a 2D conformal field theory is also a sigma model, it will satisfy these conditions if and only if its target space is compact.