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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-04-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| 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. |
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| ISSN: | 1029-8479 |