2025/12/04 by Tseytlin, Arkady A., Wang, Zihan
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2512.04948
We review and elaborate on the issue of 3d world volume supersymmetry that appears as a residual part of global target space supersymmetry in the BST supermembrane action. While there is no direct ``spinning membrane'' analog of the world-volume supersymmetric spinning string action that could be obtained by coupling D copies of 3d scalar multiplet to 3d supergravity, we discuss how one may construct an N=1 3d supersymmetric analog of the derivative expansion of the bosonic membrane action in static gauge. We compare the resulting N=1 supersymmetric action for eight 3d scalar multiplets to the N=8 3d supersymmetric action describing the D=11 supermembrane in the static gauge. The two actions are not equivalent which is related to the fact that the full N=8 supersymmetry of the static-gauge D=11 supermembrane action can be realised only if the fermions are described by an SO(8) spinor rather than vector. The two actions are still directly related in special dimensions D=4 and 5. We also compute the one-loop world-volume scattering amplitudes for the two theories, finding that they indeed agree for D=4,5 but disagree for D=11.