A critical look at ${\hat{I}}^2$-function singularities at large $N$

Abstract

We propose a self-consistency equation for the ${\hat{I}}^2$-function for theories with a large number of flavours, $N$, that exploits all the available information in the Wilson-Fisher critical exponent, $\ddot{I}‰$, truncated at a fixed order in $1/N$. We show that singularities appearing in critical exponents do not necessarily imply singularities in the ${\hat{I}}^2$-function. We apply our method to (non-)abelian gauge theory, where $\ddot{I}‰$ features a negative singularity. The singularities in the ${\hat{I}}^2$-function and in the fermion mass anomalous dimension are simultaneously removed providing no hint for a UV fixed point in the large-$N$ limit.

5 pages, 3 figures. v2 matches the published version