On RG potential in Yang-Mills theories

TL;DR

This paper constructs an RG potential for N=2 supersymmetric SU(2) Yang-Mills theory, demonstrating the RG flow is gradient and discussing potential changes after supersymmetry breaking, highlighting challenges in matching automorphic functions to perturbation theory.

Contribution

It introduces a gradient RG potential for the theory and analyzes the implications of supersymmetry breaking on the RG flow.

Findings

RG flow is gradient in N=2 supersymmetric SU(2) Yang-Mills

Constructed a positive definite metric from the RG potential

Discussed the impact of supersymmetry breaking on the flow

Abstract

We construct an RG potential for N=2 supersymmetric SU(2) Yang-Mills theory, and extract a positive definite metric by comparing its gradient with the recently discovered beta-function for this system, thus proving that the RG flow is gradient in this four-dimensional field theory. We also discuss how this flow might change after supersymmetry breaking, provided the quantum symmetry group does not, emphasizing the non-trivial problem of asymptotic matching of automorphic functions to perturbation theory.