hep-th/9410nnn Relevant Perturbations Of The SU(1, 1)/U(1) Coset

It is shown that the space of cohomology classes of the SU(1, 1)/U(1) coset at negative level k contains states of relevant conformal dimensions. These states correspond to the energy density operator of the associated nonlinear sigma model. We exhibit that there exists a subclass of relevant operators forming a closed fusion algebra. We make use of these operators to perform renormalizable perturbations of the SU(1, 1)/U(1) coset. In the infra-red limit, the perturbed theory flows to another conformal model. We identify one of the perturbative conformal points with the SU(2)/U(1) coset at positive level. From the point of view of the string target space geometry, the given renormalization group flow maps the euclidean black hole geometry described by the SU(1, 1)/U(1) coset into the sphere described by the SU(2)/U(1) coset.