The local renormalization of super-Yang-Mills theories

TL;DR

This paper develops a method for the consistent local renormalization of $ abla$-supersymmetric Yang-Mills theories, introducing a space-time-dependent scale and revealing exact perturbative structures in $ abla$-supersymmetric models.

Contribution

It introduces a framework for local renormalization in super-Yang-Mills theories with a space-time-dependent scale, including an exact perturbative action in $ abla$-supersymmetric cases.

Findings

The renormalized action includes derivatives of the holomorphic coupling.

The $ abla$-supersymmetric $ ext{N}=2$ theory's action is exact at all orders.

A holomorphic scheme is used for consistent renormalization.

Abstract

We show how to consistently renormalize $\mathcal{N} = 1$ and $\mathcal{N} = 2$ super-Yang-Mills theories in flat space with a local (i.e. space-time-dependent) renormalization scale in a holomorphic scheme. The action gets enhanced by a term proportional to derivatives of the holomorphic coupling. In the $\mathcal{N} = 2$ case, this new action is exact at all orders in perturbation theory.