Assess whether melonic F-extrema are maxima

Ascertain whether, in melonic large-N conformal field theories, the extremum obtained by F-extremization is generically a maximum (as in supersymmetric cases), and determine the conditions under which such a maximizing principle holds.

Background

For SCFTs with four supercharges, the authors review that F- or a-maximization yields a maximum at the conformal fixed point when the theory is unitary. By contrast, in melonic theories, the extremum need not be a maximum, and multiple extrema (maxima, minima, saddles) can occur.

They explicitly state that it is not yet clear whether an analogous maximization principle holds in melonic settings, highlighting an unresolved aspect of the F-extremization program outside supersymmetry.