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

TL;DR

This paper introduces a new eleven-dimensional gauge theory for the M Algebra, constructed via Abelian Semigroup Expansion of osp(32|1), providing a Lorentz-invariant Lagrangian with a novel symmetric tensor.

Contribution

It establishes a novel link between the M Algebra and osp(32|1) using Abelian Semigroup Expansion and constructs a new gauge-invariant Lagrangian in eleven dimensions.

Findings

Derived an M Algebra-invariant symmetric tensor of rank six.

Constructed a Lorentz-invariant gauge Lagrangian for the M Algebra.

Linked M Algebra to osp(32|1) through a systematic expansion method.

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.