Softly Broken N=2 QCD with Massive Quark Hypermultiplets, I

TL;DR

This paper analyzes all soft breakings of N=2 supersymmetric QCD with SU(2) gauge group and various hypermultiplet flavors, using Seiberg-Witten solutions and elliptic functions to understand the effective couplings and monodromy properties.

Contribution

It provides a comprehensive method to determine couplings and monodromies in softly broken N=2 QCD with hypermultiplets, extending the Seiberg-Witten framework.

Findings

Explicit expressions for effective couplings in softly broken theories

Analysis of monodromy properties via embedding into higher rank gauge theories

Approximate effective potential formulas for moderate supersymmetry breaking

Abstract

We present a general analysis of all the possible soft breakings of N=2 supersymmetric QCD, preserving the analytic properties of the Seiberg-Witten solutions for the SU(2) group with Nf=1, 2, 3 hypermultiplets. We obtain all the couplings of the spurion fields in terms of properties of the Seiberg-Witten periods, which we express in terms of elementary elliptic functions by uniformizing the elliptic curves associated to each number of flavors. We analyze in detail the monodromy properties of the softly broken theory, and obtain them by a particular embedding into a pure gauge theory with higher rank group. This allows to write explicit expressions of the effective potential, which are close to the exact answer for moderate values of the supersymmetry breaking parameters. The vacuum structures and phases of the broken theories will be analyzed in the forthcoming second part of this paper.