Line of Fixed Points in Gross-Neveu Theories

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, characterized by an exactly marginal sextic interaction. We determine the conformal window of UV-complete theories, universal scaling dimensions, and the phase diagram using renormalization 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.

  • Received 22 July 2022
  • Revised 6 April 2023
  • Accepted 28 April 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.201602

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

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