Line of Fixed Points in Gross-Neveu Theories

TL;DR

This paper demonstrates that in three-dimensional Gross-Neveu theories with many fermion flavors, a line of UV fixed points exists characterized by an exactly marginal sextic interaction, with implications for conformal field theory and holography.

Contribution

It identifies a line of interacting UV fixed points in 3D Gross-Neveu theories and explores their properties using renormalisation group methods, revealing new aspects of their phase structure.

Findings

Existence of a line of UV fixed points in the sextic Gross-Neveu theory.

Determination of the conformal window and universal scaling dimensions.

Massless theories can generate mass without discrete symmetry breaking.

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.