Renormalization group in 2 + ∈ dimensions and ∈ → 2: A simple model analysis

Nobuaki Nagao, Hiroshi Suzuki

Research output: Contribution to journalArticle

Abstract

Using a simple solvable model, i.e., the Higgs-Yukawa system with an infinite number of flavors, we explicitly demonstrate how a dimensional continuation of the β function in the two dimensional MS scheme fails to reproduce the correct behavior of the β function in four dimensions. The mapping between coupling constants in the two dimensional MS scheme and a conventional scheme in the cutoff regularization, in which the dimensional continuation of the β function is smooth, becomes singular when the dimension of spacetime approaches four. The existence of a non-trivial fixed point in 2 + ∈ dimensions continued to four dimensions (∈→2) in the two dimensional MS scheme is spurious and asymptotic safety cannot be imposed on this model in four dimensions.

Original languageEnglish
Pages (from-to)985-993
Number of pages9
JournalProgress of Theoretical Physics
Volume95
Issue number5
DOIs
Publication statusPublished - May 1996
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

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