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String backgrounds associated with gauged $G/H$ WZNW models genericallydepend on $\alpha'$ or $1/k$. The exact expressions for the correspondingmetric $G_{\m\n}$, antisymmetric tensor $B_{\m\n}$, and dilaton $\phi$ can beobtained by eliminating the $2d$ gauge field from the local part of theeffective action of the gauged WZNW model. We show that there exists amanifestly gauge-invariant prescription for the derivation of the antisymmetrictensor coupling. When the subgroup $H$ is one-dimensional and $G$ is simple theantisymmetric tensor is given by the semiclassical ($\alpha'$-independent)expression. We consider in detail the simplest non-trivial example withnon-trivial $B_{\m\n}$ -- the D=3 sigma model corresponding to the $[SL(2,R) xR]/R$ gauged WZNW theory (`charged black string') and show that the exactexpressions for $G_{\m\n}$, $B_{\m\n}$ and $\phi$ solve the Weyl invarianceconditions in the two-loop approximation. Similar conclusion is reached for theclosely related $SL(2,R)/R$ chiral gauged WZNW model. We find that there existsa scheme in which the semiclassical background is also a solution of thetwo-loop conformal invariance equations (but the tachyon equation takes anon-canonical form). We discuss in detail the role of field redefinitions(scheme dependence) in establishing a correspondence between the sigma modeland conformal field theory results.Comment: 55 pages, harvmac, CERN-TH.6969/93, THU-93/25, Imperial/TP/92-93/59.  (Another prescription for extracting the exact antisymmetric tensor is  described leading to a purely semiclassical expression for it

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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Antisymmetric tensor coupling and conformal invariance inσmodels corresponding to gauged WZNW theories