SU(2) Yang-Mills Theory with extended Supersymmetry in a Background Magnetic Field

TL;DR

This paper investigates the vacuum structure of N=2 and N=4 supersymmetric Yang-Mills theories in a background magnetic field, comparing perturbative and non-perturbative effects to understand their effective potentials.

Contribution

It provides a detailed analysis of the effective potential in SUSY Yang-Mills theories, incorporating instanton effects and dual descriptions to understand non-perturbative phenomena.

Findings

Non-perturbative monopoles eliminate non-trivial minima in the strong-coupling regime.

Dual descriptions yield a self-consistent effective potential across all background fields.

Instanton effects significantly influence the vacuum structure in N=2 SUSY Yang-Mills.

Abstract

The vacuum structure of N=2 (and N=4) SUSY Yang-Mills theory is analyzed in detail by considering the effective potential for constant background scalar- magnetic fields within different approximations. We compare the one-loop approximation with- or without instanton improved effective coupling with the one-loop result in the dual desription. For N=2 we find that non-perturbative monopole degrees of freedom remove the non-trivial minima present in the (improved) one-loop potential in the strong-coupling regime. The combination of Yang-Mills and dual desription leads to a self-consistent effective potential over the full range of background fields.