The infrared or ultraviolet scale for a gauge theory

Abstract

We propose a conjecture that leads to the determination of the intrinsic scale (the scale at which the coupling constant diverges) for any gauge theory by comparison to another theory for which there is phenomenological information, provided that the two theories are placed in the same space-time volume. This conjecture is verified independently for $U(1)_{em}$ and for $QCD$. In this framework and from this perspective we show that the group $SO(10)$ is the only viable candidate among the supersymmetric GUT groups $SU(5)$, $SO(10)$ and $E_6$.