Duality Symmetry in Softly Broken N=2 Gauge Theories

TL;DR

This paper investigates the effects of soft breaking of N=2 supersymmetric gauge theories to N=0, analyzing duality symmetry, vacuum structure, and RG equations, with explicit formulas and numerical studies for SU(2).

Contribution

It provides explicit Seiberg-Witten period formulas for SU(2) and explores the duality symmetry and vacuum phases in softly broken N=2 theories, extending results to other classical gauge groups.

Findings

Softly broken models exhibit duality symmetry behavior.

Stable vacua are confining despite duality symmetry.

Derived RG equations for self-dual gauge theories.

Abstract

We study the soft breaking of N=2 self-dual gauge theories down to N=0 by promoting the coupling constant and hypermultiplet masses to spurions, and we analyze the microscopic duality symmetry in the resulting models. Explicit formulae are given for the Seiberg-Witten periods and couplings in the case of SU(2), and we perform a numerical study of the non-supersymmetric vacuum structure in the case of the mass-deformed N=4 SU(2) gauge theory. Although the softly broken model has a well-defined behavior under the duality symmetry, the stable vacua are in a confining phase. We also extend some of the results to the self-dual theories with classical gauge groups, and we obtain the RG equation for these models.