One-point functions of the Lagrangian in $\mathcal{N}=4$ SYM with boundaries, defects and interfaces

Abstract

We obtain one-point functions of the ambient Lagrangian $\mathcal{O}_{\mathcal{L}}$ in $\mathcal{N}=4$ SYM with $\frac{1}{2}$-BPS boundaries, defects and interfaces classified by Gaiotto and Witten, which include maximally supersymmetric Janus interfaces and BCFTs relevant for double holography, as well as for Janus interfaces with reduced supersymmetry. For Janus interfaces we extend recent results capturing $\langle \mathcal{O}_{\mathcal{L}}\rangle$ in certain limits to exact dependence on $N$ and $λ$, and confirm a non-renormalization conjecture. We also clarify recent results for Janus variants preserving less supersymmetry. For general $\frac{1}{2}$-BPS Gaiotto-Witten theories with genuine defect degrees of freedom we derive one-point functions using supersymmetric localization, confirm that the results agree with holographic predictions in the appropriate limits, and show that the one-point functions in general exhibit non-trivial coupling dependence.