Lorerift-covariant non-Abelian gauging of a supermembrane

We perform the Lorentz-covariant non-Abelian gauging of a supermembrane (M-2 brane) action. This is a generalization of our previous work based on the teleparallel formulation, in which Lorentz covariance was not manifest. We introduce the Killing supervector xi(AI) with the adjoint index I for a non-Abelian gauge group H. This formulation,is applicable to the compactification of a supermembrane from 11 dimensions into D dimensions, such as H = SO(11-D) for the compactification M-11 -> S11-D X M-D(1 <= D <= 9).