BPS spectrum on AdS3×S3×S3×S1

The BPS spectrum of string theory on AdS3 × S3 × S3 × S1 is determined using a world-sheet description in terms of WZW models. It is found that the theory only has BPS states with j+ = j− where j± refer to the spins of the su2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathfrak{s}\mathfrak{u}(2) $$\end{document} algebras of the large 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 superconformal algebra. We then re-examine the BPS spectrum of the corresponding supergravity and find that, contrary to previous claims in the literature, also in supergravity only the states with j+ = j− are BPS. This resolves a number of long-standing puzzles regarding the BPS spectrum of string theory and supergravity in this background.