One-point functions for doubly-holographic BCFTs and backreacting defects

We derive one-point functions in 4d N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 4 SYM with 12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \frac{1}{2} $$\end{document}-BPS boundaries, defects and interfaces which host large numbers of defect degrees of freedom. The theories are engineered by Gaiotto-Witten D3/D5/NS5 brane setups with large numbers of D5 and NS5 branes, and have holographic duals with fully backreacted 5-branes. They include BCFTs with 3d SCFTs on the boundary which allow for the notion of double holography, as well as D3/D5 defects and interfaces with large numbers of D5-branes. Through a combination of supersymmetric localization and holography we derive one-point functions for 4d chiral primary operators.