Nonperturbative Renormalization Group Equation and Beta Function in N=2 SUSY Yang-Mills

TL;DR

This paper derives the exact nonperturbative beta function for N=2 supersymmetric SU(2) Yang-Mills theory and establishes a corresponding Renormalization Group Equation, advancing understanding of nonperturbative quantum field dynamics.

Contribution

It provides the first exact nonperturbative beta function and RG equation for N=2 SUSY Yang-Mills, linking the beta function to the prepotential's behavior.

Findings

Exact beta function for N=2 SUSY SU(2) Yang-Mills

Nonperturbative RG equation derived

Connection between beta function and prepotential

Abstract

We obtain the exact beta function for $N=2$ SUSY $SU(2)$ Yang-Mills theory and prove the nonperturbative Renormalization Group Equation $$ \partial_\Lambda{\cal F}(a,\Lambda)= {\Lambda\over \Lambda_0}\partial_{\Lambda_0}{\cal F}(a_0,\Lambda_0) e^{-2\int_{\tau_0}^\tau {dx \beta^{-1}(x)}}. $$