Flow equation for Halpern-Huang directions of scalarmodels
- 20 February 2001
- journal article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 63 (6)
- https://doi.org/10.1103/physrevd.63.065011
Abstract
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.Comment: 18 pages, 4 figures, LaTeX, references added, presentation improved, final version to appear in Phys. Rev.Keywords
Other Versions
This publication has 18 references indexed in Scilit:
- ASYMPTOTIC FREEDOM IN A SCALAR FIELD THEORY ON THE LATTICEModern Physics Letters A, 1998
- Halpern and Huang Reply:Physical Review Letters, 1996
- Comment on “Fixed-Point Structure of Scalar Fields”Physical Review Letters, 1996
- Analytical solutions of exact renormalization group equationsNuclear Physics B, 1996
- Nontrivial directions for scalar fieldsPhysical Review D, 1996
- NATURAL SLOW-ROLL INFLATIONModern Physics Letters A, 1996
- Fixed-Point Structure of Scalar FieldsPhysical Review Letters, 1995
- Critical exponents from the effective average actionNuclear Physics B, 1994
- Exact evolution equation for the effective potentialPhysics Letters B, 1993
- Renormalization Group Equation for Critical PhenomenaPhysical Review A, 1973