Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-01-24
Phys.Rev.Lett. 77 (1996) 1658
Physics
High Energy Physics
High Energy Physics - Theory
Typos corrected. A Comment - to be published in Phys. Rev. Lett. 1 page, 1 eps figure, uses LaTeX, RevTex and epsf
Scientific paper
10.1103/PhysRevLett.77.1658
In a recent Letter (K.Halpern and K.Huang, Phys. Rev. Lett. 74 (1995) 3526), certain properties of the Local Potential Approximation (LPA) to the Wilson renormalization group were uncovered, which led the authors to conclude that $D>2$ dimensional scalar field theories endowed with {\sl non-polynomial} interactions allow for a continuum of renormalization group fixed points, and that around the Gaussian fixed point, asymptotically free interactions exist. If true, this could herald very important new physics, particularly for the Higgs sector of the Standard Model. Continuing work in support of these ideas, has motivated us to point out that we previously studied the same properties and showed that they lead to very different conclusions. Indeed, in as much as the statements in hep-th/9406199 are correct, they point to some deep and beautiful facts about the LPA and its generalisations, but however no new physics.
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