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

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

1996-01-12

arxiv.org/abs/hep-th/9601061v2

Prog.Theor.Phys. 95 (1996) 985-994

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, PHYZZX. English is improved, some references are added

Scientific paper

10.1143/PTP.95.985

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 $\beta$ function in two dimensional MS scheme {\it fails\/} to reproduce the correct behavior of the $\beta$ 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 $\beta$ function is smooth, becomes singular when the dimension of spacetime approaches to four. The existence of a non-trivial fixed point in $2+\epsilon$ dimensions continued to four dimensions $\epsilon\to2$ 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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