Stringy membranes in AdS/CFT

We study membrane configurations in AdS7/4 × S4/7. The membranes are wrapped around the compact manifold S4/7 and are dynamically equivalent to bosonic strings in AdS5. We thus conveniently identify them as “stringy membranes”. For the case of AdS7 × S4, their construction is carried out by embedding the Polyakov action for classical bosonic strings in AdS5, into the corresponding membrane action. Therefore, every string configuration in AdS5 can be realized by an appropriately chosen stringy membrane in AdS7 × S4. We discuss the possibility of this being also the case for stringy membranes in AdS4 × S7/\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{\mathbb{Z}}^k} $\end{document} (k ≥ 1). By performing a stability analysis to the constructed solutions, we find that the (membrane) fluctuations along their transverse directions are organized in multiple Lamé stability bands and gaps in the space of parameters of the configurations. In this membrane picture, strings exhibit a single band/gap structure.