Is a truly marginal perturbation of the $G_k\times G_k$ WZNW model at $k=-2c_V(G)$ an exception to the rule?

TL;DR

The paper demonstrates a unique marginal deformation of a specific WZNW model that challenges existing criteria, and constructs a continuous family of such models, revealing new insights into conformal field theory.

Contribution

It identifies a truly marginal deformation of the $G_k imes G_k$ WZNW model at a special level that defies the Chaudhuri-Schwartz criterion, and constructs a continuous family of models.

Findings

Existence of a marginal deformation that violates the Chaudhuri-Schwartz criterion.

Construction of a continuous family of WZNW models at a specific level.

Identification of a special case in conformal field theory.

Abstract

It is shown that there exists a truly marginal deformation of the direct sum of two $G_k$ WZNW models at $k=-2c_V(G)$ (where $c_V(G)$ is the eigenvalue of the quadratic Casimir operator in the adjoint representation of the group $G$) which does not seem to fit the Chaudhuri-Schwartz criterion for truly marginal perturbations. In addition, a continuous family of WZNW models is constructed.