A Non-renormalization Theorem for the Wilsonian Gauge Couplings in Supersymmetric Theories

TL;DR

This paper proves that in certain supersymmetric gauge theories, the Wilsonian gauge coupling's beta-function is exactly determined at one loop, with no higher-order or non-perturbative corrections, extending previous results.

Contribution

It establishes a non-renormalization theorem for the Wilsonian gauge couplings in supersymmetric theories, showing the beta-function is one-loop exact.

Findings

Beta-function is exhausted at 1-loop

No higher-loop or non-perturbative contributions

Extends the Shifman-Vainshtein result

Abstract

We show that the holomorphic Wilsonian beta-function of a renormalizable asymptotically free supersymmetric gauge theory with an arbitrary semi-simple gauge group, matter content, and renormalizable superpotential is exhausted at 1-loop with no higher loops and no non-perturbative contributions. This is a non-perturbative extension of the well known result of Shifman and Vainshtein.