A polynomial Weyl-invariant spinning-membrane action

A review of the construction of a Weyl-invariant spinning-membrane action that is polynomial in the fields, without a cosmological constant term, comprised of quadratic and quartic-derivative terms, and where supersymmetry is linearly realized, is presented. The action is invariant under a modified supersymmetry transformation law which is derived from a new Q+K+S sum-rule based on the 3D-superconformal algebra.