Coupling running through the looking-glass of dimensional reduction

This is the authors' abstract. We don't add key points for this paper.

The dimensional reduction, in a form of transition from four to two dimensions, was used in the 90s of the past century in a context of the HE Regge scattering. Recently, it has got a new impetus in quantum gravity where it opens the way to renormalizability and finite short-distance behaviour. We consider a QFT model gφ4 with running coupling defined in both domains of different dimensionality; the g (q 2) evolutions being duly correlated at the reduction scale q ∼ M. Beyond this scale, in the deep UV 2-dimensional region, the running coupling does not increase any more. Instead, it slightly decreases and tends to a finite value g 2(∞) < g 2(M 2) from above. As a result, the global evolution picture looks quite peculiar and proposes a base for the modified scenario of gauge couplings behavior with UV fixed points provided by dimensional reduction instead of leptoquarks.