Chiral anomaly as a composite operator in the gradient flow exact renormalization group formalism

Abstract

Abstract The gradient flow exact renormalization group (GFERG) is an idea that incorporates gauge-invariant gradient flows into the formalism of the exact renormalization group (ERG). GFERG introduces a Wilson action with a cutoff while keeping the vector gauge invariance manifestly. The details of the formalism are still to be worked out. In this paper, we apply GFERG to construct the Wilson action of massless Dirac fermions under the background chiral gauge fields. By formulating the chiral anomaly as a “composite operator”, we make the scale invariance of the anomaly manifest. We argue that the same result extends to QCD.