Vacuum Alignment with more Flavors

Abstract

We study the alignment of the vacuum in gauge theories with $N_f$ Dirac fermions transforming according to a complex representation of the gauge group. The alignment of the vacuum is produced by adding a small mass perturbation to the theory. We study in detail the $N_f=2,3$ and $4$ case. For $N_f=2$ and $N_f=3$ we reproduce earlier known results including the Dashen phase with spontaneous violation of the combined charge conjugation and parity symmetry, CP. For $N_f=4$ we find regions with and without spontaneous CP violation. We then generalize to an arbitrary number of flavors. Here it is shown that at the point where $N_f-1$ flavors are degenerate with positive mass $m>0$ and the mass of the $N_f$'th flavor becomes negative and equal to $-m$ CP breaks spontaneously.

arXiv commentCoincides with published version. Several new results for an arbitrary number of flavors. New plot added

References in corpus (29)

• Orientifold theory dynamics and symmetry breaking
• Walking in the SU(N)
• Supersymmetry Inspired QCD Beta Function
• UV and IR Zeros of Gauge Theories at The Four Loop Order and Beyond
• Higher-Loop Corrections to the Infrared Evolution of a Gauge Theory with Fermions
• Conformal Windows of SU(N) Gauge Theories, Higher Dimensional Representations and The Size of The Unparticle World
• Aspects of Chiral Symmetry and the Lattice
• Quark Masses and Chiral Symmetry
• Two Lectures on Technicolor
• Beta Function and Anomalous Dimensions
• Spontaneous violation of CP symmetry in the strong interactions
• Study of Possible Ultraviolet Zero of the Beta Function in Gauge Theories with Many Fermions
• Ambiguities in the up quark mass
• Instantons and the Chiral Phase Transition
• Comparison of Some Exact and Perturbative Results for a Supersymmetric SU($N_c$) Gauge Theory
• Higher Loop Corrections to the Infrared Evolution of Fermionic Gauge Theories in the RI' Scheme
• Infrared Fixed Points in the minimal MOM Scheme
• CP Violation and Flavor Mixing in Technicolor Theories
• Conformal House
• Exceptional and Spinorial Conformal Windows
• Renormalization-Group Flows and Fixed Points in Yukawa Theories
• Infrared Evolution and Phase Structure of a Gauge Theory Containing Different Fermion Representations
• Pion masses in 2-flavor QCD with $\eta$ condensation
• Vacuum Alignment in Technicolor Theories-I. The Technifermion Sector
• Quark masses, the Dashen phase, and gauge field topology
• Accidental Goldstone Bosons
• A New Mechanism for Light Composite Higgs Bosons
• a New Conformal Window Bound from the a theorem
• Chiral Vacuum Alignment and Spontaneous CP Violation by Four-Fermi Operators