Non-geometric BPS branes on T-folds

We give a detailed (microscopic) description of the geometric and non-geometric fundamental branes and their bound states in Type II superstring compactifications preserving 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} = 6 supersymmetry. We consider general boundary states that couple to the twisted sector and compute the relevant annulus amplitudes. We check consistency of the construction by relating the 'transverse' channel, corresponding to closed-string 'tree-level' exchange, with the 'direct' open-string loop channel. Focussing on the Type IIA frame, we show that D0-D4 have the expected tension for a geometric brane, while the non-geometric D2-D6 boundary states have a tension equal to 1/K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ 1/\sqrt{K} $$\end{document} the one of a geometric brane for the ZK orbifold. This is consistent with Fricke T-duality of the 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} = 6 model.