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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2025-04-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP04(2025)085 |
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| author | Ludo Fraser-Taliente John Wheater |
| author_facet | Ludo Fraser-Taliente John Wheater |
| author_sort | Ludo Fraser-Taliente |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-38ee089e534a493badce78745aee99b2 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-38ee089e534a493badce78745aee99b22025-08-20T03:52:53ZengSpringerOpenJournal of High Energy Physics1029-84792025-04-012025414010.1007/JHEP04(2025)085F-extremization determines certain large-N CFTsLudo Fraser-Taliente0John Wheater1Rudolf Peierls Centre for Theoretical Physics, University of OxfordRudolf Peierls Centre for Theoretical Physics, University of OxfordAbstract 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.https://doi.org/10.1007/JHEP04(2025)0851/N ExpansionRenormalization GroupNonperturbative EffectsRenormalization and Regularization |
| spellingShingle | Ludo Fraser-Taliente John Wheater F-extremization determines certain large-N CFTs Journal of High Energy Physics 1/N Expansion Renormalization Group Nonperturbative Effects Renormalization and Regularization |
| title | F-extremization determines certain large-N CFTs |
| title_full | F-extremization determines certain large-N CFTs |
| title_fullStr | F-extremization determines certain large-N CFTs |
| title_full_unstemmed | F-extremization determines certain large-N CFTs |
| title_short | F-extremization determines certain large-N CFTs |
| title_sort | f extremization determines certain large n cfts |
| topic | 1/N Expansion Renormalization Group Nonperturbative Effects Renormalization and Regularization |
| url | https://doi.org/10.1007/JHEP04(2025)085 |
| work_keys_str_mv | AT ludofrasertaliente fextremizationdeterminescertainlargencfts AT johnwheater fextremizationdeterminescertainlargencfts |