ANTISYMMETRIC TENSOR COUPLING AND CONFORMAL-INVARIANCE IN SIGMA-MODELS CORRESPONDING TO GAUGED WZNW THEORIES

String backgrounds associated with gauged G/H WZNW models generically depend on alpha' or 1/k. The exact expressions for the corresponding m etric G(munu), antisymmetric tensor B(munu) and dilaton phi can be obt ained by eliminating the two-dimensional gauge field from the local pa rt of the effective action of the gauged WZNW model. We show that ther e exists a manifestly gauge-invariant prescription for the derivation of the antisymmetric tensor coupling and discuss some subtleties invol ved. When the subgroup H is one dimensional and G is simple the antisy mmetric tensor is given by the semiclassical (alpha'-independent) expr ession. We consider in detail the simplest nontrivial example with B(m unu) not-equal 0, the D = 3 sigma model corresponding to the [SL(2,R) X R ]/R gauged WZNW theory (''charged black string''), and show that t he exact expressions for G(munu), B(munu) and phi solve the Weyl invar iance conditions in the two-loop approximation. A similar conclusion i s reached for the closely related SL(2,R)/R chiral gauged WZNW model. We find that there exists a scheme in which the semiclassical backgrou nd is also a solution of the two-loop conformal invariance equations ( but the tachyon equation takes a noncanonical form). We discuss in det ail the role of field redefinitions (scheme dependence) in establishin g a correspondence between the sigma model and conformal field theory results.