Boundary F-maximization

TL;DR

The paper proposes a boundary analogue of the F-theorem for four-dimensional CFTs with half-BPS boundaries, defining a boundary free energy F_{\partial} from hemisphere and sphere partition functions and conjecturing that F_{\partial} decreases along boundary RG flows while the IR boundary R-symmetry maximizes F_{\partial}. It analyzes several concrete setups, including perturbative BCFTs, a free conformally coupled scalar, and free vector multiplets, using localization and effective 3d reductions to test the conjecture and illustrate how boundary conditions and interfaces fit into F_{\partial}-maximization. The work connects boundary F-maximization to 3d F-maximization via doubling and localization, provides explicit computations and transformation properties under S-duality, and lays out a program to extend to non-Abelian bulk SCFTs. Overall, it provides evidence and a clear framework for a boundary F-theorem and F-maximization principle, with several calculable tests and a roadmap for future proofs.

Abstract

We discuss a variant of the F-theorem and F-maximization principles which applies to (super)conformal boundary conditions of 4d (S)CFTs.