On "spinning" membrane models

Several alternative actions for a bosonic membrane have recently been proposed. We show that a linearly realized locally world-volume-supersymmetric (spinning membrane) extension of any of these actions implies an analogous extension of the standard Dirac membrane action. We further show that a (Minkowski) spacetime Lorentz-covariant spinning membrane action (that reduces to the Dirac membrane action when all fermions vanish) cannot be constructed within the framework of the three-dimensional super-Poincaré tensor calculus.