Conformal field theories from deformations of theories with Wn symmetry

Abstract

We construct a set of nonrational conformal field theories that consist of deformations of Toda field theory for sl(n). In addition to preserving conformal invariance, the theories may still exhibit a remnant infinite-dimensional affine symmetry. The case n=3 is used to illustrate this phenomenon, together with further deformations that yield enhanced Kac-Moody symmetry algebras. For generic n we compute N-point correlation functions on the Riemann sphere and show that these can be expressed in terms of sl(n) Toda field theory ((N-2)n+2)-point correlation functions.