On The Beta-Function in N=2 Supersymmetric Yang-Mills Theory

TL;DR

This paper demonstrates that under certain symmetry and flow assumptions, the non-perturbative beta-function in N=2 supersymmetric Yang-Mills theory can be uniquely determined from its weak coupling behavior, aligning with Seiberg-Witten results.

Contribution

It shows that assuming the commutativity of renormalization group flow with duality symmetry suffices to derive the non-perturbative beta-function from weak coupling data.

Findings

Non-perturbative beta-function matches Seiberg-Witten calculations.

Symmetry and flow assumptions uniquely determine the beta-function.

Results confirm the consistency of duality and renormalization group analysis.

Abstract

The constraints of N=2 supersymmetry, in combination with several other quite general assumptions, have recently been used to show that N=2 supersymmetric Yang-Mills theory has a low energy quantum parameter space symmetry characterised by the discrete group $\gu$. We show that if one also assumes the commutativity of renormalization group flow with the action of this group on the complexified coupling constant $\ta$, then this is sufficient to determine the non-perturbative $\beta$-function, given knowledge of its weak coupling behaviour. The result coincides with the outcome of direct calculations from the Seiberg-Witten solution.