  We investigate in the simplest compact D=4 N=1 Type IIB orientifold models
the sigma-model symmetry suggested by the proposed duality of these models to
heterotic orbifold vacua. This symmetry is known to be present at the classical
level, and is associated to a composite connection involving untwisted moduli
in the low-energy supergravity theory. In order to study possible anomalies
arising at the quantum level, we compute potentially anomalous one-loop
amplitudes involving gluons, gravitons and composite connections. We argue that
the effective vertex operator associated to the composite connection has the
same form as that for a geometric deformation of the orbifold. Assuming this,
we are able to compute the complete anomaly polynomial, and find that all the
anomalies are canceled through a Green-Schwarz mechanism mediated by twisted RR
axions, as previously conjectured. Some questions about the field theory
interpretation of our results remain open.
