Large N flavor beta-functions: a recap

$β$-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 $Nα$, and there are also various indications as to the nature of higher order effects. The singularity structure as a function of $Nα$ has implications for the existence of nontrivial fixed points.

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