Critical Look at β -Function Singularities at Large N

We propose a self-consistency equation for the β functions for theories with a large number of flavors, N, that exploits all the available information in the Wilson-Fisher critical exponent, ω, truncated at a fixed order in 1/N. We show that singularities appearing in critical exponents do not necessarily imply singularities in the β function. We apply our method to (non-)Abelian gauge theory, where ω features a negative singularity. The singularities in the β function and in the fermion mass anomalous dimension are simultaneously removed providing no hint for a UV fixed point in the large-N limit.