Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.
The tricritical Ising CFT and conformal bootstrap,
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Local CFTs extremise $F$
Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.
- $\phi^6$ at $6$ (and some $8$) loops in $3d$