On New Conformal Field Theories with Affine Fusion Rules

TL;DR

This paper constructs new unitary conformal field theories with affine fusion rules using free bosons and parafermions, revealing extended W-algebras analogous to affine algebras and providing exact character formulas.

Contribution

It introduces explicit realizations of conformal data with affine fusion rules through free boson and parafermion systems, establishing their unitarity and algebraic structure.

Findings

Constructed unitary conformal field theories with affine fusion rules.

Derived exact character formulas for these theories.

Demonstrated the extended W-algebras as analogues of affine algebras.

Abstract

Some time ago, conformal data with affine fusion rules were found. Our purpose here is to realize some of these conformal data, using systems of free bosons and parafermions. The so constructed theories have an extended $W$ algebras which are close analogues of affine algebras. Exact character formulae is given, and the realizations are shown to be full fledged unitary conformal field theories.