On world-volume supersymmetry of supermembrane action in static gauge

Abstract We review and elaborate on the issue of three-dimensional (3D) world-volume supersymmetry that appears as a residual part of global target space supersymmetry in the Bergshoeff–Sezgin–Townsend (BST) supermembrane action. While there is no direct ‘spinning membrane’ analogue 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 analogue 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 realized 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.