Coupling running through the Looking-Glass of dimensional Reduction

TL;DR

This paper explores how dimensional reduction from four to two dimensions affects the running coupling in a quantum field theory, revealing a finite UV fixed point and suggesting a new scenario for gauge coupling behavior.

Contribution

It introduces a model coupling in different dimensions with conjugated evolutions at the reduction scale, showing a finite UV fixed point due to dimensional reduction.

Findings

The running coupling decreases and tends to a finite value in the deep UV.

Dimensional reduction leads to a finite UV fixed point for the coupling.

Proposes a modified gauge coupling scenario with UV fixed points from dimensional reduction.

Abstract

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.