Confinement, Supersymmetry Breaking and Theta Parameter Dependence in the Seiberg-Witten Model

Abstract

By using the standard perturbation theory we study the mass as well as $\theta$ parameter dependence of the Seiberg-Witten theory with $SU(2)$ gauge group, supplemented with a $N=1$ supersymmetric as well as a smaller nonsupersymmetric (e.g.) gaugino mass. Confinement persists at all values of the bare vacuum parameter ${\theta }_{ph}$; as it is varied there is however a phase transition at ${\theta }_{ph}=-\pi ,\pi ,3\pi ,\dots$. At these values of ${\theta }_{ph}$ the vacuum is doubly degenerate and CP invariance is spontaneously broken à la Dashen. Due to the instanton-induced renormalization effect the low energy effective $\theta$ parameter remains small irrespectively of ${\theta }_{ph}$ as long as the gaugino mass is sufficiently small.

8 pages, Latex file

References in corpus (3)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Some comments on $N=2$ supersymmetric Yang-Mills

Cited by in corpus (33)

• Reading between the lines of four-dimensional gauge theories
• Theta, Time Reversal, and Temperature
• Theta dependence of SU(N) gauge theories in the presence of a topological term
• On Supersymmetry Breaking in String Theory and its Realization in Brane Worlds
• N=2 supersymmetric dynamics for pedestrians
• Dynamical Symmetry Breaking in Supersymmetric SU(n_c) and USp(2n_c) Gauge Theories
• Towards N=1 Super-Yang-Mills on the Lattice
• Evidence for a Non-Supersymmetric 5d CFT from Deformations of 5d $SU(2)$ SYM
• Some Exact Results in QCD-like Theories
• $\theta =\pi$ in $SU(N)/{\mathbb{Z}}_N$ gauge theories
• More Exact Results on Chiral Gauge Theories: the Case of the Symmetric Tensor
• Isomonodromic Properties of the Seiberg-Witten Solution
• Probing the dynamics of chiral SU(N) gauge theories via generalized anomalies
• The Spectrum of Softly Broken N=1 Supersymmetric Yang-Mills Theory
• CP, Charge Fractionalizations and Low Energy Effective Actions in the SU(2) Seiberg-Witten Theories with Quarks
• Oblique Confinement at $\theta \ne 0$ in weakly coupled gauge theories with deformations
• Gauge Enhanced Quantum Criticality and Time Reversal Domain Wall: SU(2) Yang-Mills Dynamics with Topological Terms
• The Field Theory of Non-Supersymmetric Brane Configurations
• $\theta$ and the ${\eta }^{\prime }$ in Large $N$ Supersymmetric QCD
• Softly Broken MQCD and the Theta Angle
• Demonstration of Confinement and Chiral Symmetry Breaking in $SO(N_c)$ Gauge Theories
• Confinement and duality in supersymmetric gauge theories
• Renormalization Group and Dynamics of Supersymmetric Gauge Theories
• The Phases of Non-supersymmetric Gauge Theories: the $SO(N_c)$ Case Study
• Duality Symmetry in Softly Broken N=2 Gauge Theories
• Renormalization of the vacuum angle in quantum mechanics, Berry phase and continuous measurements
• On Confinement Index
• Gauge interactions and topological phases of matter
• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD
• Generalized symmetry enriched criticality in (3+1)d
• Vacuum Structure of Softly Broken N=1 Supersymmetric QCD
• Softly Broken SQCD: in the Continuum, on the Lattice, on the Brane
• Quark Condensates in Non-Supersymmetric MQCD