CONFORMAL SIGMA-MODELS CORRESPONDING TO GAUGED WESS-ZUMINO-WITTEN THEORIES

We develop a field-theoretical approach to the determination of the ba ckground target space fields corresponding to general G/H coset confor mal theories described by gauged WZW models. The basic idea is to iden tify the effective action of a gauged WZW theory with the effective ac tion of a sigma model. The derivation of the quantum effective action in the gauged WZW theory is presented in detail, both in the bosonic a nd in the supersymmetric cases. We explain why and how one can truncat e the effective action by omitting most of the non-local terms (thus p roviding a justification for some previous suggestions). The resulting metric, dilaton and the antisymmetric tensor are non-trivial function s of 1/k (or alpha') and represent a large class of conformal sigma mo dels. The exact expressions for the fields in the supersymmetric case are equal to the leading order (''semiclassical'') bosonic expressions (with no shift of k). An explicit form in which we find the sigma mod el couplings makes it possible to prove that the metric and the dilato n are equivalent to the fields which are obtained in the operator appr oach, i.e. by identifying the L0-operator of the conformal theory with a Klein-Gordon operator in a background. The metric can be considered as a ''deformation' of an invariant metric on the coset space G/H and the dilaton can be in general represented in terms of the logarithm o f the ratio of the determinants of the ''deformed'' and ''round'' metr ics.