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 neces...

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Bibliographic Details
Published in:Physical review letters 2019-09, Vol.123 (13), p.131602-131602, Article 131602
Main Authors: Alanne, Tommi, Blasi, Simone, Dondi, Nicola Andrea
Format: Article
Language:English
Subjects:
Fermions
Gauge theory
Singularities
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Summary: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.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.123.131602