On a Generalization of GKO Coset Construction of Conformal Field Theories

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 $s=2$.