Meromorphic Scaling Flow of N=2 Supersymmetric SU(2) Yang-Mills with Matter

TL;DR

This paper derives modular form beta-functions for N=2 SUSY SU(2) Yang-Mills theory with massless matter, analyzing their behavior across different coupling regimes and discussing mass effects.

Contribution

It introduces a meromorphic scaling flow framework with modular form beta-functions for N=2 SUSY gauge theories including matter fields.

Findings

Beta-functions are modular forms of weight -2.

Correct asymptotic behavior at fixed points.

Discusses mass effects on beta-functions.

Abstract

Beta-functions are derived for the flow of N=2 SUSY SU(2) Yang-Mills in 4-dimensions with massless matter multiplets in the fundamental representation of the gauge group. The beta-functions represent the flow of the couplings as the VEV of the Higgs field is lowered and are modular forms of weight -2. They have the correct asymptotic behaviour at both the strong and weak coupling fixed points. Corrections to the massless beta-functions when masses are turned on are discussed.