Eleven-Dimensional Gauge Theory for the M Algebra as an Abelian Semigroup Expansion of osp(32|1)

An eleven-dimensional gauge theory for the M Algebra is put forward. The gauge-invariant lagrangian belongs to the class of transgression lagrangians, which modify Chern--Simons theory with the addition of a regularizing boundary term. The M Algebra-invariant tensor needed in order to write down the transgression lagrangian comes from regarding the Algebra as an Abelian Semigroup Expansion of the orthosymplectic algebra osp(32|1). The lagrangian is displayed in an explicitly Lorentz-invariant way by means of a transgression-specific subspace separation method based on the extended Cartan homotopy formula. The lower-dimensional dynamics produced by the theory is shown to be tightly constrained, but allowing for nonzero torsion might help break the chains. Symmetrical boundary conditions directly derived from the action are considered, and some alternatives to solve them are provided. We also comment on a possible physical interpretation of the two-connection setting inherent to any transgression gauge field theory