F-extremization determines certain large-N CFTs

• Published in: The journal of high energy physics Vol. 2025; no. 4; pp. 85 - 40
• Main Authors: Fraser-Taliente, Ludo, Wheater, John
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 11.04.2025; Springer Nature B.V; SpringerOpen
• Subjects: 1/N Expansion; Classical and Quantum Gravitation; Elementary Particles; Energy; Feynman diagrams; Free energy; High energy physics; Nonperturbative Effects; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Renormalization and Regularization; Renormalization Group; String Theory; Symmetry; Tensors; 1; Renormalization Group; Expansion; Nonperturbative Effects; Renormalization and Regularization
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP04(2025)085

A bstract 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 Z S d , 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. The universal part of F ~ interpolates in continuous dimension between the known C -functions, so we can 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.