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

Abstract

A new Lagrangian realizing the symmetry of the M Algebra in eleven-dimensional space-time is presented. By means of the novel technique of Abelian Semigroup Expansion, a link between the M Algebra and the orthosymplectic algebra osp(32|1) is established, and an M Algebra-invariant symmetric tensor of rank six is computed. This symmetric invariant tensor is a key ingredient in the construction of the new Lagrangian. The gauge-invariant Lagrangian is displayed in an explicitly Lorentz-invariant way by means of a subspace separation method based on the extended Cartan homotopy formula.

arXiv comment11 pages, 1 figure. v3: updated notation and terminology; published version

References in corpus (17)

• Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity
• Expanding Lie (super)algebras through abelian semigroups
• M-Theory as a Holographic Field Theory
• New Gauge Supergravity in Seven and Eleven Dimensions
• GAMMA: A Mathematica package for performing gamma-matrix algebra and Fierz transformations in arbitrary dimensions
• Transgression forms and extensions of Chern-Simons gauge theories
• Lie-algebra expansions, Chern-Simons theories and the Einstein-Hilbert lagrangian
• Extensions, expansions, Lie algebra cohomology and enlarged superspaces
• Poincare invariant gravity with local supersymmetry as a gauge theory for the M-algebra
• The Extended Cartan Homotopy Formula and a Subspace Separation Method for Chern--Simons Theory
• A covariant formalism for Chern-Simons gravity
• On Transgression Forms and Chern--Simons (Super)gravity
• The linear spectrum of OSp(32|1) Chern-Simons supergravity in eleven dimensions
• Transgression forms as unifying principle in field theory
• Towards a Chern-Simons M theory of $OSp(1|32)\times OSp(1|32)$
• (Super-)Gravities of a different sort
• Supermatrix models for M-theory based on osp(1|32,R)

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