Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-04-09
Phys.Part.Nucl.Lett.7:379-383,2010
Physics
High Energy Physics
High Energy Physics - Theory
8 pages, 4 figures,Version to match the one which (besides the Appendix) will appear in "Particles and Nuclei (PEPAN), Letters
Scientific paper
10.1134/S1547477110060014
The dimensional reduction, in a form of transition from four to two dimensions, was used in the 90s in a context of HE Regge scattering. Recently, it got a new impetus in quantum gravity where it opens the way to renormalizability and finite short-distance behavior. We consider a QFT model $g\,\varphi^4\,$ with running coupling defined in both the two domains of different dimensionality; the $\gbar(Q^2)\,$ evolutions being duly conjugated at the reduction scale $\,Q\sim M.$ Beyond this scale, in the deep UV 2-dim region, the running coupling does not increase any more. Instead, it {\it slightly decreases} and tends to a finite value $\gbar_2(\infty) \,< \, \gbar_2(M^2)\,$ from above. As a result, the global evolution picture looks quite peculiar and can propose a base for the modified scenario of gauge couplings behavior with UV fixed points provided by dimensional reduction instead of leptoquarks.
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