On field redefinitions and exact solutions in string theory

Abstract

String backgrounds associated with gauged $G/H$ WZNW models in general depend non-trivially on $α'$. We note, however, that there exists a local covariant $\a'$-dependent field redefinition that relates the exact metric-dilaton background corresponding to the $SL(2,R)/U(1)$ model to its leading-order form ($D=2$ black hole). As a consequence, there exists a `scheme' in which the string effective equations have the latter as an exact solution. However, the corresponding equation for the tachyon (which, like other Weyl anomaly coefficients, has scheme-dependent form) still contains corrections of all orders in $α'$. As a result, the `probes' (the tachyons) still feel the $α'$-corrected background. The field redefinitions we discuss contain the dilaton terms in the metric transformation law. We comment on exact forms of the duality transformation in different `schemes'.

11 pages, harvmac, CERN-TH.6970/93 [ A new section on tachyonic equation is added: while there exists a scheme where the exact D=2 `black hole' metric-dilaton background has semiclassical form, the equation for the tachyon still contains α'-corrections, i.e. the tachyon still feels the α'-corrected background ]