Year: 2025
Type: article
Abstract: 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 $$ {Z}_{S^d} $$ Z S d , called $$ \overset{\sim }{F} $$ 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 $$ \overset{\sim }{F} $$ 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.
Source: Journal of High Energy Physics
Authors: Ludo Fraser-Taliente, John Wheater
Institution: University of Oxford
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Funder: University of Oxford
OpenAlex ID: W4409378863