  String backgrounds associated with gauged $G/H$ WZNW models generically
depend on $\alpha'$ or $1/k$. The exact expressions for the corresponding
metric $G_{\m\n}$, antisymmetric tensor $B_{\m\n}$, and dilaton $\phi$ can be
obtained by eliminating the $2d$ gauge field from the local part of the
effective action of the gauged WZNW model. We show that there exists a
manifestly gauge-invariant prescription for the derivation of the antisymmetric
tensor coupling. When the subgroup $H$ is one-dimensional and $G$ is simple the
antisymmetric tensor is given by the semiclassical ($\alpha'$-independent)
expression. We consider in detail the simplest non-trivial example with
non-trivial $B_{\m\n}$ -- the D=3 sigma model corresponding to the $[SL(2,R) x
R]/R$ gauged WZNW theory (`charged black string') and show that the exact
expressions for $G_{\m\n}$, $B_{\m\n}$ and $\phi$ solve the Weyl invariance
conditions in the two-loop approximation. Similar conclusion is reached for the
closely related $SL(2,R)/R$ chiral gauged WZNW model. We find that there exists
a scheme in which the semiclassical background is also a solution of the
two-loop conformal invariance equations (but the tachyon equation takes a
non-canonical form). We discuss in detail the role of field redefinitions
(scheme dependence) in establishing a correspondence between the sigma model
and conformal field theory results.
