On a Generalization of GKO Coset Construction of Conformal Field Theories

TL;DR

This paper generalizes the GKO coset construction in conformal field theories by introducing a scaled affine subalgebra, demonstrated through the Ising CFT example, expanding the theoretical framework of CFT models.

Contribution

It proposes a new generalized GKO coset construction using scaled affine subalgebras, broadening the scope of conformal field theory models.

Findings

Introduces a scaled affine subalgebra in GKO construction.

Analyzes the Ising CFT as a generalized GKO coset.

Provides insights into the structure of scaled coset models.

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 $s=2$.