Perturbed Gauged WZNW Models

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.