UV and IR Zeros of Gauge Theories at The Four Loop Order and Beyond

TL;DR

This paper analyzes the phase diagram of gauge theories at four-loop order, identifying fixed points and anomalous dimensions, and suggests the potential for a nontrivial ultraviolet fixed point at large flavor numbers.

Contribution

It provides a comprehensive classification of zeros of the beta function at four-loop order and explores the existence of ultraviolet fixed points using all-orders beta function analysis.

Findings

Identification of a rich phase diagram with multiple fixed points

Calculation of anomalous dimensions at infrared fixed points

Evidence for possible ultraviolet fixed points at large flavor numbers

Abstract

We unveil the general features of the phase diagram for any gauge theory with fermions transforming according to distinct representations of the underlying gauge group, at the four-loop order. We classify and analyze the zeros of the perturbative beta function and discover the existence of a rich phase diagram. The anomalous dimension of the fermion masses, at the infrared stable fixed point, are presented. We show that the infrared fixed point, and associated anomalous dimension, are well described by the all-orders beta function for any theory. We also argue the possible existence, to all orders, of a nontrivial ultraviolet fixed point for gauge theories at large number of flavors.