F-extremization determines certain large-N CFTs

Journal article

We show that the conformal data of a range of large-N CFTs, the melonic CFTs, are specified by constrained extremization of the universal part of the sphere free energy F = − log ZSd , called F˜. This family includes the generalized SYK models, the vector models (O(N), Gross-Neveu, etc.), and the tensor field theories. The known F and a-maximization procedures in SCFTs are therefore extended to these non-supersymmetric CFTs in continuous d. We establish our result using the two-particle irreducible (2PI) effective action, and, equivalently, by Feynman diagram resummation. F˜ interpolates in continuous dimension between the known C-functions, so we interpret this result as an extremization of the number of IR degrees of freedom, in the spirit of the generalized c, F, a-theorems. The outcome is a complete classification of the melonic CFTs: they are the conformal mean field theories which extremize the universal part of the sphere free energy, subject to an IR marginality condition on the interaction Lagrangian.

Authors: Fraser-Taliente, L; Wheater, J

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Journal of High Energy Physics
• Volume: 2025
• Issue: 4
• Article number: 85
• Publication date: 2025-04-11
• Acceptance date: 2025-03-07
• DOI: 10.1007/jhep04(2025)085
• EISSN: 1029-8479
• ISSN: 1126-6708
• Language: English
• Keywords: 1/N expansion; renormalization group; nonperturbative effects; renormalization and regularization