Supermembranes

The supersymmetric M2-brane worldvolume theory includes embedding bosons and fermions and has kappa symmetry. In eleven dimensions its fermionic embedding coordinate is a thirty-two-component Majorana spinor.

The first term uses the induced worldvolume metric from the supervielbein; the second is the Wess-Zumino brane coupling to the super-three-form. Its fermionic dependence is retained before bosonic truncation. The relative charge magnitude equals the brane tension, while $q=\pm 1$ sets the orientation and matching kappa symmetry projector sign. In an on-shell eleven-dimensional supergravity superspace, this action has kappa symmetry.