On a Generalization of GKO Coset Construction of Conformal Field Theories

Abstract

We introduce a generalization of Goddard-Kent-Olive (GKO) coset construction of two dimensional conformal field theories based on a choice of a scaled affine subalgebra ${\hat{\mathfrak{h}}}^s$ of a given affine Lie algebra $\hat{\mathfrak{h}}$. We study some aspects of the construction through the example of Ising CFT as a generalized GKO coset of ${\text{su(2)}}_1$ with a scaling factor $s=2$.

arXiv commentThis paper has been withdrawn by the author as it came to his knowledge that exactly the same construction has been introduced before by Kac and Wakimoto in Acta Appl. Math.21(1990)3, and studied by P.Bouwknegt in arXiv:q-alg/9610013