Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.
Heckman and Tom Rudelius,Evidence for C-theorems in 6D SCFTs, [arXiv:1506.06753pdf], [Inspire]
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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.