Given enough supersymmetry, the IR limits of certain quantum field theories can be solved by extremizing a quantity associated to the sphere free energy $F=-\log Z_{S^d}$ over a space of trial data, subject to a constraint. This constraint effectively enforces the marginality of the interaction term in the IR. The tensorial quantum field theories admit a large-$N$ limit dominated by the melonic graphs; we show that their IR limits, the melonic CFTs, are determined by an identical constrained extremization principle. $F$ has been suggested as a counting of the number of degrees of freedom of a field theory, so we can understand this as: "as much 'stuff' as possible, given a constraint."
