Tensionless supersymmetric M2 branes in \(AdS_4 \times S^7\) and Giant Diabolo

We find various supersymmetric configurations of toroidal M2 brane solutions in \(\AdS_4 \times S^7\) or, more generally, in \(\AdS_4 \times S^7/Z_k\). In this class we identify solutions preserving 1/4 and 1/8 supersymmetries of the background. The supersymmetric M2 branes have angular momenta and winding on \(S^7\), and null world-volumes. In certain cases they collapse to string-like configurations. These configurations can be viewed as a higher-dimensional (membrane) analog of BMN states. We compute the energy and angular momenta, showing that all supersymmetric configurations obey the BPS relation \(E=J/R \),\ \(J= \sum_{i=1}^4 |J_i|\) with \(E, J\to \infty \). Finally, we also study another class of supersymmetric M2-branes, including uncompact rotating membranes of "diabolo" shape.