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arXiv · 1905.08709

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

Tommi Alanne·Simone Blasi·Nicola Andrea Dondi
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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.

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Tommi Alanne, Simone Blasi, Nicola Andrea Dondi. 2019-05-21. A critical look at $\beta$-function singularities at large $N$. https://doi.org/10.1103/physrevlett.123.131602

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