The Conformal Anomaly and a new Exact RG

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.