Conformal field theories from deformations of theories with $W_n$ symmetry

TL;DR

This paper constructs new non-rational conformal field theories derived from Toda theories with $W_n$ symmetry, revealing preserved affine symmetries and expressing correlation functions in terms of Toda theory.

Contribution

It introduces a class of deformed non-rational CFTs with affine symmetry, extending Toda theories and providing explicit correlation function formulas.

Findings

Deformed theories maintain conformal and affine symmetries.

Correlation functions are expressible via Toda field theory.

Enhanced symmetries appear in specific deformations.

Abstract

We construct a set of non-rational conformal field theories that consist of deformations of Toda field theory for sl(n). Besides conformal invariance, the theories still enjoy 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 correlation functions.