Critical Ising correlation functions in the plane and on the torus

Explicit expressions are given for all correlation functions of spin, disorder and energy operators of the critical Ising model in the plane or on the torus. Formulae for insertions of energy-momentum tensors may also be written, giving access to correlation functions of secondary fields. Two alternative methods are used throughout the paper: bosonization of the fermion representation of the Ising model or use of the free field (orbifold) interpretation of the Ashkin-Teller model. Many identities result from the consistency between these alternative approaches.