Melonic large-N CFTs are exactly the conformal mean field theories that extremize the universal part of the sphere free energy under linear IR marginality constraints.
A note on the SYK model with complex fermions
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We consider a version of the Sachdev-Ye-Kitaev model with complex fermions. We apply the shadow formalism to find four-point functions in the leading order in $1/N$ and dimensions of operators present in the theory. We also compute the retarded kernel and show that the Lyapunov exponent for the mode corresponding to the $U(1)$ charge is zero.
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$F$-extremization determines certain large-$N$ CFTs
Melonic large-N CFTs are exactly the conformal mean field theories that extremize the universal part of the sphere free energy under linear IR marginality constraints.