Remarks on the Existence of Spinning Membrane Actions

It has been recently argued by some authors that is impossible to construct a Weyl invariant spinning membrane action, where the S-supersymmetry associated with the 3D superconformal algebra, is relinquished without gauge fixing. Contrary to those assertions, we show why it is possible to construct a Weyl-invariant spinning polynomial membrane action , without curvature terms, where both the conformal boost symmetry and S-supersymmetry are explicitly broken by the action. It is shown that the gauge algebra closes despite that the two latter symmetries are broken . For this to happen, a modifed Q-supersymmetry transformation is required that generates the compensating terms to cancel the spurious contributions from the S and conformal boost anomalous transformations. A substantial discussion of the quantization of the spinning membrane and anomalies is given. We review briefly the role that this spinning membrane action may have in the theory of D-branes, Skyrmions and BPS monopoles in the large N -limit of SU(N) Yang-Mills .