Perturbed Gauged WZNW Models

TL;DR

This paper introduces a new class of unitary perturbations for conformal theories based on gauged WZNW models, revealing how sigma model perturbations connect nonunitary and unitary models and lead to perturbed coset constructions.

Contribution

It presents a novel BRST invariant sigma model perturbation approach that generates perturbed coset models, including a specific case equivalent to Zamolodchikov's minimal series perturbation.

Findings

Nonunitary level k WZNW model perturbed by sigma model term becomes unitary level -k model.

Perturbed gauged WZNW models no longer describe coset constructions.

Identifies a BRST invariant perturbation equivalent to Zamolodchikov's ,1 perturbation.

Abstract

We discuss a new type of unitary perturbations around conformal theories inspired by the $\sigma$-model perturbation of the nonunitary WZNW model. We show that the nonunitary level $k$ WZNW model perturbed by its sigma model term goes to the unitary level $-k$ WZNW model. When plugged into the gauged WZNW model the given perturbation results in the perturbed gauged WZNW model which no longer describes a coset construction. We consider the BRST invariant generalization of the sigma model perturbation around the gauged WZNW model. In this way we obtain perturbed coset constructions. In the case of the $SU_{m-2}(2)\times SU_1(2)/SU_{m-1}(2)$ coset, the BRST invariant sigma model perturbation is identical to Zamolodchikov's $\Phi_{(3,1)}$ perturbation of the minimal conformal series. The existence of general geometry flows is clarified.