### 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 language | English |
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Pages (from-to) | 985-993 |

Number of pages | 9 |

Journal | Progress of Theoretical Physics |

Volume | 95 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 1996 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)