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arXiv · hep-th/9601061

Renormalization Group in $2+ε$ Dimensions and $ε\to2$: A simple model analysis

Nobuaki Nagao·Hiroshi Suzuki
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Abstract

Using a simple solvable model, i.e., Higgs--Yukawa system with an infinite number of flavors, we explicitly demonstrate how a dimensional continuation of the $β$ function in two dimensional MS scheme {\it fails\/} to reproduce the correct behavior of the $β$ function in four dimensions. The mapping between coupling constants in 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 to four. The existence of a non-trivial fixed point in $2+ε$ dimensions continued to four dimensions $ε\to2$ in the two dimensional MS scheme is spurious and the asymptotic safety cannot be imposed to this model in four dimensions.

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Nobuaki Nagao, Hiroshi Suzuki. 1996-01-16. Renormalization Group in $2+ε$ Dimensions and $ε\to2$: A simple model analysis. https://doi.org/10.1143/ptp.95.985

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