Exact renormalization group equation in presence of rescaling anomaly

TL;DR

This paper revisits Wilson's renormalization group approach in supersymmetric Yang-Mills theory, accounting for the Konishi anomaly, and derives an exact RG equation that incorporates anomaly effects and reproduces the known beta-function relation.

Contribution

It explicitly computes the Wilsonian action for N=1 SUSY Yang-Mills with a gauge-invariant regularization, including anomaly contributions, refining the understanding of RG flow in supersymmetric theories.

Findings

Wilsonian action includes non-anomalous and anomaly-induced terms

The anomaly term obeys Polchinski's flow equation

Reproduces the Shifman-Vainshtein beta-function relation

Abstract

Wilson's approach to renormalization group is reanalyzed for supersymmetric Yang-Mills theory. Usual demonstration of exact renormalization group equation must be modified due to the presence of the so called Konishi anomaly under the rescaling of superfields. We carry out the explicit computation for N=1 SUSY Yang-Mills theory with the simpler, gauge invariant regularization method, recently proposed by Arkani-Hamed and Murayama. The result is that the Wilsonian action S_M consists of two terms, i.e. the non anomalous term, which obeys Polchinski's flow equation and Fujikawa-Konishi determinant contribution. This latter is responsible for Shifman-Vainshtein relation of exact beta-function.