CP, Charge Fractionalizations and Low Energy Effective Actions in the SU(2) Seiberg-Witten Theories with Quarks

TL;DR

This paper investigates the dynamical properties, charge fractionalizations, and low-energy effective actions of SU(2) Seiberg-Witten theories with quarks, revealing phenomena like confinement, chiral symmetry breaking, and oblique confinement, and analyzing their consistency under supersymmetry breaking.

Contribution

It provides a detailed analysis of the singularities, CP invariance, and charge fractionalizations in SU(2) Seiberg-Witten models with quarks, including effects of perturbations and soft supersymmetry breaking.

Findings

Charge fractionalization consistent with semiclassical analysis

Confinement and chiral symmetry breaking at singularities

Oblique confinement observed in specific vacua for N_f=3

Abstract

Several dynamical aspects of the SU(2) Seiberg-Witten models with N_f quark hypermultiplets are explored. We first clarify the meaning of the number of the singularities of the space of vacua. CP invariance of the theories are then studied and periodicities of theories in \theta with and without bare quark masses are obtained ((4-N_f)\pi and \pi, respectively). CP noninvariance at a generic point of QMS manifests itself as the electric and quark-number charge fractionalizations for the dyons; we show that the exact Seiberg-Witten solution contains such effects correctly, in agreement with the semiclassical analysis recently made by F.Ferrari. Upon N=1 perturbation the low energy effective theories at the singularities display confinement, and in most cases chiral symmetry breaking as a consequence. In one of the vacua for N_f=3 confinement is not accompanied by chiral symmetry breaking: we interpret it as an example of oblique confinement of 't Hooft. We discuss further the consistency of the physical picture found here by studying the effects of soft supersymmetry breaking as well as the behavior of the theory in the N=1 limit.