Dynamical Higgs Mechanism without Elementary Scalars: A Lesson from Instantons

Abstract

The generation of gauge--dependent fermion vacuum condensates in Yang--Mills theory would dynamically break the gauge symmetry and thus provide an alternative to the Higgs mechanism in unified theories. We explore a simple example: instanton-induced quark pair (diquark) condensation in QCD with 2 flavors and $N_c$ colors. We do find diquark condensates in the vacuum, but only for $N_c = 2$, where they are equivalent to the standard quark-antiquark condensate. At $N_c \geq 3$ diquark condensates exist as meta--stable saddle points of the instanton-induced effective QCD action and may strongly affect the properties of matter under extreme conditions. The scalar diquark excitation, which is a Goldstone boson at $N_c =2$, becomes unbound for $N_c \geq 3$.