  It was argued recently that conformal invariance in flat spacetime implies
Weyl invariance in a general curved background for unitary theories and
possible anomalies in the Weyl variation of scalar operators are identified. We
argue that generically unitarity alone is not sufficient for a conformal field
theory to be Weyl invariant. Furthermore, we show explicitly that when a
unitary conformal field theory couples to gravity in a Weyl invariant way, each
primary scalar operator that is either relevant or marginal in the unitary
conformal field theory corresponds to a Weyl-covariant operator in the curved
background.
