Antisymmetric tensor coupling and conformal invariance in sigma models corresponding to gauged WZNW theories

Details Antisymmetric tensor coupling and conformal invariance in sigma models corresponding to gauged WZNW theories Antisymmetric tensor coupling and conformal invariance in sigma models corresponding to gauged WZNW theories

1993-10-23

arxiv.org/abs/hep-th/9310159v2

Phys.Rev.D49:2933-2956,1994

Physics

High Energy Physics

High Energy Physics - Theory

55 pages, harvmac, CERN-TH.6969/93, THU-93/25, Imperial/TP/92-93/59. (Another prescription for extracting the exact antisymmet

Scientific paper

10.1103/PhysRevD.49.2933

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.

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