Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.
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Conformal ladder integrals are represented via thermal free energies of massive scalars, obey a second-order differential equation in even dimensions at any loop order, and admit an all-loop resummation for arbitrary D.
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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.
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A thermal representation for conformal ladder integrals
Conformal ladder integrals are represented via thermal free energies of massive scalars, obey a second-order differential equation in even dimensions at any loop order, and admit an all-loop resummation for arbitrary D.