F-maximization along the RG flows: a proposal

TL;DR

This paper extends the F-maximization principle to non-superconformal theories using a Lagrange multiplier approach, providing a new method to analyze RG flows in various gauge theories.

Contribution

It introduces a novel extension of F-maximization incorporating Lagrange multipliers to account for non-superconformal effects, inspired by four-dimensional analogs.

Findings

Validated the proposal in multiple gauge group examples

Demonstrated the Lagrange multiplier's role analogous to coupling constants

Provided a framework for analyzing RG flows beyond superconformal cases

Abstract

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.