Line of Fixed Points in Gross-Neveu Theories

Abstract

In the limit of many fermion flavors it is demonstrated that the sextic Gross-Neveu theory in three dimensions displays a line of interacting UV fixed points, characterised by an exactly marginal sextic interaction. We determine the conformal window of UV-complete theories, universal scaling dimensions, and the phase diagram using renormalisation group methods. Massless theories arise naturally, and the generation of mass proceeds without the breaking of a discrete symmetry. Striking similarities with critical scalar theories at large $N$ are highlighted, and implications from the viewpoint of conformal field theory and the AdS/CFT conjecture are indicated.

6 pages, 4 figures; v2: reasoning and Fig. 2 improved, accepted for publication with Physical Review Letters

References in corpus (9)

• Exact evolution equation for the effective potential
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Asymptotic safety guaranteed
• Asymptotic safety: a simple example
• Asymptotic safety guaranteed in supersymmetry
• Critical $O(N)$ models in the complex field plane
• Asymptotic safety with Majorana fermions and new large N equivalences
• Non-Gaussian fixed points in fermionic field theories without auxiliary Bose-fields
• Critical Fermions with Spontaneously Broken Scale Symmetry

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