Conformally exact black hole perturbed by a marginal operator

We have examined the theories that are induced by gauged WZW models, by adding the tachyon field as a marginal operator. It can be seen that the original configurations give by WZW models should be modified in order to make the theory full-conformally invariant. It has been found that 2d is a critical dimension in the sense that the metric obtained from gauged WZW is modified by the tachyon condensation for d > 2, but not for d ⩽ 2.