Coupling running through the looking-glass of dimensional reduction

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 $ bar g $ bar 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 $ bar g $ bar g ₂(∞) < $ bar g $ bar 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.