A critical look at $\beta$-function singularities at large $N$

Abstract

We propose a self-consistency equation for the $\beta$-function for theories with a large number of flavours, $N$, that exploits all the available information in the Wilson-Fisher critical exponent, $\omega$, truncated at a fixed order in $1/N$. We show that singularities appearing in critical exponents do not necessarily imply singularities in the $\beta$-function. We apply our method to (non-)abelian gauge theory, where $\omega$ features a negative singularity. The singularities in the $\beta$-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

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• Model Building from Asymptotic Safety with Higgs and Flavor Portals
• Safety versus triviality on the lattice
• Towards the QED beta function and renormalons at $1/N_f^2$ and $1/N_f^3$
• Asymptotically safe dark matter with gauged baryon number
• Perturbative Asymptotic Safety and Its Phenomenological Applications
• Spectral Functions of Gauge Theories with Banks-Zaks Fixed Points
• Peccei-Quinn Symmetry Breaking via Asymptotically Safe Dynamical Scalegenesis: A Walking Axicolor and Axion
• Large $N_f$ for multiple representations
• Conformal Windows beyond Asymptotic Freedom