Universality of spontaneous chiral symmetry breaking in gauge theories

Abstract

We investigate one-flavor QCD with an additional chiral scalar field. For a large domain in the space of coupling constants, this model belongs to the same universality class as QCD, and the effects of the scalar become unobservable. This is connected to a ``bound-state fixed point'' of the renormalization flow for which all memory of the microscopic scalar interactions is lost. The QCD domain includes a microscopic scalar potential with minima at nonzero field. On the other hand, for a scalar mass term m^2 below a critical value m_c^2, the universality class is characterized by perturbative spontaneous chiral symmetry breaking which renders the quarks massive. Our renormalization group analysis shows how this universality class is continuously connected with the QCD universality class.

33 pages, 6 figures, v2: presentation improved, results unchanged, version to appear in PRD

References in corpus (12)

• Exact evolution equation for the effective potential
• On the Infrared Exponent for Gluon and Ghost Propagation in Landau Gauge QCD
• Instantons at work
• Non-perturbative Landau gauge and infrared critical exponents in QCD
• Renormalization Flow of Bound States
• Infrared Exponents and Running Coupling of SU(N) Yang-Mills Theories
• Running coupling in Yang-Mills theory - a flow equation study -
• Phase transition and critical behaviour of the d=3 Gross-Neveu model
• Renormalisation group flows for gauge theories in axial gauges
• Flow Equations without Mean Field Ambiguity
• Running coupling constant and propagators in SU(2) Landau gauge
• Phenomenological tests for the freezing of the QCD running coupling constant

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