F-extremization determines certain large-N CFTs

Abstract 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 F ~ $$ \overset{\sim }{F} $$ . This family includes the generalized SYK models, t...

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Bibliographic Details
Main Authors: Ludo Fraser-Taliente, John Wheater
Format: Article
Language:English
Published: SpringerOpen 2025-04-01
Series:Journal of High Energy Physics
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Online Access:https://doi.org/10.1007/JHEP04(2025)085
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Summary:Abstract 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 F ~ $$ \overset{\sim }{F} $$ . 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 ~ $$ \overset{\sim }{F} $$ 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.
ISSN:1029-8479