# The infrared or ultraviolet scale for a gauge theory

## TL;DR

This paper introduces a conjecture to determine the intrinsic scale of gauge theories by comparing them to phenomenologically known theories, verified for QED and QCD, and applies it to evaluate grand unified theories.

## Contribution

It proposes a novel conjecture linking gauge theory scales to phenomenological data, and assesses the viability of GUT groups using this approach.

## Key findings

- The conjecture is verified for QED and QCD.
- Among supersymmetric GUT groups, SO(10) is identified as the only viable candidate.
- The method provides a new way to determine gauge theory scales.

## 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 $E_6$.