Minimal Models with Integrable Local Defects

TL;DR

This paper develops a general framework for constructing integrable defect theories by perturbing conformal field theories with local defect operators, extending the classification of integrable models to include various minimal and coset theories.

Contribution

It introduces a novel method to classify and construct integrable defect theories as perturbations of conformal field theories, including minimal models and coset theories based on SO(2n).

Findings

Classified integrable defect theories for all $c<1$ minimal models.

Mapped the Ising model defect to an orbifolded sine-Gordon theory.

Connected defect operators to known models like the Kondo model.

Abstract

We describe a general way of constructing integrable defect theories as perturbations of conformal field theory by local defect operators. The method relies on folding the system onto a boundary field theory of twice the central charge. The classification of integrable defect theories obtained in this way parallels that of integrable bulk theories which are a perturbation of the tensor product of two conformal field theories. These include local defect perturbations of all $c<1$ minimal models, as well as of the coset theories based on SO(2n), obtained in this way. We discuss in detail the former case of all the Virasoro minimal models. In the Ising case our construction corresponds to having a spin field as a defect operator; in the folded formulation this is mapped onto an orbifolding of the boundary sine-Gordon theory at $\beta^2/8\pi = 1/8$, or a version of the anisotropic Kondo model.