Stringy Membranes in AdS/CFT

TL;DR

This paper introduces 'Stringy Membranes' in AdS/CFT, showing how membrane configurations in higher-dimensional AdS spaces can emulate string dynamics in lower dimensions, with stability properties analyzed through Lamé band structures.

Contribution

It demonstrates that classical string configurations in AdS_5 can be realized as membrane configurations in AdS_7xS^4, extending the AdS/CFT correspondence framework.

Findings

Membrane configurations can replicate string dynamics in AdS_5.

Stability analysis reveals Lamé band/gap structures in membrane fluctuations.

Strings exhibit a simpler single band/gap structure compared to membranes.

Abstract

We study membrane configurations in AdS_{7/4}xS^{4/7}. The membranes are wrapped around the compact manifold S^{4/7} and are dynamically equivalent to bosonic strings in AdS_5. We thus conveniently identify them as "Stringy Membranes". For the case of AdS_7xS^4, their construction is carried out by embedding the Polyakov action for classical bosonic strings in AdS_5, into the corresponding membrane action. Therefore, every string configuration in AdS_5 can be realized by an appropriately chosen stringy membrane in AdS_7xS^4. We discuss the possibility of this being also the case for stringy membranes in AdS_4xS^7/Z^k (k > 1 or 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 Lam\'{e} stability bands and gaps in the space of parameters of the configurations. In this membrane picture, strings exhibit a single band/gap structure.