  For scalar field theory, a new generalization of the Exact RG to curved space
is proposed, in which the conformal anomaly is explicitly present. Vacuum terms
require regularization beyond that present in the canonical formulation of the
Exact RG, which can be accomplished by adding certain free fields, each at a
non-critical fixed-point. Taking the Legendre transform, the sole effect of the
regulator fields is to remove a divergent vacuum term and they do not
explicitly appear in the effective average action. As an illustration, both the
integrated conformal anomaly and Polyakov action are recovered for the Gaussian
theory in d=2.
