Duality in deformed coset fermionic models

TL;DR

This paper investigates the duality properties of the deformed $SU(2)_k/U(1)$-parafermion model, revealing a symmetry that exchanges order and disorder operators and identifying special points where conformal invariance is restored.

Contribution

It formulates the perturbed parafermion model as an interacting fermionic coset and uncovers a duality symmetry along with new self-dual points.

Findings

Identification of a duality symmetry exchanging spin and dual spin operators.

Recovery of conformal invariance at specific coupling constants.

Discovery of a novel self-dual point in the model.

Abstract

We study the $SU(2)_k/U(1)$-parafermion model perturbed by its first thermal operator. By formulating the theory in terms of a (perturbed) fermionic coset model we show that the model is equivalent to interacting WZW fields modulo free fields. In this scheme, the order and disorder operators of the $Z_k$ parafermion theory are constructed as gauge invariant composites. We find that the theory presents a duality symmetry that interchanges the roles of the spin and dual spin operators. For two particular values of the coupling constant we find that the theory recovers conformal invariance and the gauge symmetry is enlarged. We also find a novel self-dual point.