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F-maximization along the RG flows: a proposal
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We propose an extension of the F-maximization principle to take into account the effects of non-superconformality. Guided by a four-dimensional analog, we formulate a modification of the free energy via the Lagrange multiplier technique. We conjecture that the Lagrange multiplier plays the same role as the coupling constant, at least at weak coupling. We check our proposal in many examples with unitary, symplectic and orthogonal gauge groups.
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$F$-extremization determines certain large-$N$ CFTs
Melonic large-N CFTs are exactly the conformal mean field theories that extremize the universal part of the sphere free energy under linear IR marginality constraints.
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