Nonabelian Higgs models: paving the way for asymptotic freedom

Abstract

Asymptotically free renormalization group trajectories can be constructed in nonabelian Higgs models with the aid of generalized boundary conditions imposed on the renormalized action. We detail this construction within the languages of simple low-order perturbation theory, effective field theory, as well as modern functional renormalization group equations. We construct a family of explicit scaling solutions using a controlled weak-coupling expansion in the ultraviolet, and obtain a standard Wilsonian RG relevance classification of perturbations about scaling solutions. We obtain global information about the quasi-fixed function for the scalar potential by means of analytic asymptotic expansions and numerical shooting methods. Further analytical evidence for such asymptotically free theories is provided in the large-N limit. We estimate the long-range properties of these theories, and identify initial/boundary conditions giving rise to a conventional Higgs phase.

39 pages, 32 figures

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• Scheme dependence of asymptotically free solutions
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• Renormalization Group Flow of the Higgs Potential
• The quantum criticality of the Standard Model and the hierarchy problem
• Renormalization Flow of Nonlinear Electrodynamics
• B-Anomalies from flavorful U(1)' extensions, safely