EFFECTIVE ACTION OF THE GAUGED WZW MODEL AND EXACT STRING SOLUTIONS

We suggest how to derive the exact (all order in alpha') expressions f or the background fields for string solutions corresponding to gauged WZW models, directly at the 2d field theory level. One is first to rep lace the classical gauged WZW action by the quantum effective one and then to integrate out the gauge field. We find the explicit expression for the gauge invariant non-local effective action of the gauged WZW model. The two terms (corresponding to the group and subgroup) which a ppear with the same coefficients in the classical action get different k-dependent coefficients in the effective one. The procedure of integ rating out the gauge field is considered in detail for the SL(2, R)/U( 1) model and the exact expressions for the D = 2 metric and the dilato n (originally found in the conformal field theory approach) are reprod uced.