Lorentz-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 ξAI 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 M11→S11-DxMD(1≤D≤9)