Large N flavor beta-functions: a recap

TL;DR

This paper reviews the behavior of beta-functions in gauge theories with many flavors, focusing on large N expansions and their implications for fixed points and higher-order effects.

Contribution

It provides a comprehensive recap of the large N flavor beta-functions, including known results and indications about higher-order effects and fixed point structures.

Findings

First nontrivial order in 1/N expansion known for all Nα values

Singularity structure impacts the existence of nontrivial fixed points

Indications of higher order effects in beta-functions

Abstract

$\beta$-functions for abelian and non-abelian gauge theories are studied in the regime where the large $N$ flavor expansion is applicable. The first nontrivial order in the 1/$N$ expansion is known for any value of $N\alpha$, and there are also various indications as to the nature of higher order effects. The singularity structure as a function of $N\alpha$ has implications for the existence of nontrivial fixed points.