Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-09-06
Phys.Rev. D63 (2001) 065011
Physics
High Energy Physics
High Energy Physics - Theory
18 pages, 4 figures, LaTeX, references added, presentation improved, final version to appear in Phys. Rev. D
Scientific paper
10.1103/PhysRevD.63.065011
A class of asymptotically free scalar theories with O(N) symmetry, defined via the eigenpotentials of the Gaussian fixed point (Halpern-Huang directions), are investigated using renormalization group flow equations. Explicit solutions for the form of the potential in the nonperturbative infrared domain are found in the large-N limit. In this limit, potentials without symmetry breaking essentially preserve their shape and undergo a mass renormalization which is governed only by the renormalization group distance parameter; as a consequence, these scalar theories do not have a problem of naturalness. Symmetry-breaking potentials are found to be ``fine-tuned'' in the large-N limit in the sense that the nontrivial minimum vanishes exactly in the limit of vanishing infrared cutoff: therefore, the O(N) symmetry is restored in the quantum theory and the potential becomes flat near the origin.
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