Abelian Semigroup Expansion Research Articles

Generalized cosmological term in D=4 supergravity from a new AdS\u2013Lorentz superalgebra

A new supersymmetrization of the so-called AdS–Lorentz algebra is presented. It involves two fermionic generators and is obtained by performing an abelian semigroup expansion of the superalgebra mathfrak {osp}(4|1). The peculiar properties of the aforesaid expansion method are then exploited to construct a D=4 supergravity action involving a generalized supersymmetric cosmological term in a geometric way, only from the curvatures of the novel superalgebra. The action obtained with this procedure is a MacDowell–Mansouri like action. Gauge invariance and supersymmetry of the action are also analyzed.

Chern–Simons supergravity in [formula omitted] and Maxwell superalgebra

We present the construction of the D=3 Chern–Simons supergravity action without cosmological constant from the minimal Maxwell superalgebra sM3. This superalgebra contains two Majorana fermionic charges and can be obtained from the osp(2|1)⊗sp(2) superalgebra using the abelian semigroup expansion procedure. The components of the Maxwell invariant tensor are explicitly derived.

N=1 supergravity and Maxwell superalgebras

We present the construction of the D = 4 supergravity action from the minimal Maxwell superalgebra sℳ4, which can be derived from the $$ \mathfrak{osp}\ \left(4\Big|1\right) $$ superalgebra by applying the abelian semigroup expansion procedure. We show that N = 1, D = 4 pure supergravity can be obtained alternatively as the MacDowell-Mansouri like action built from the curvatures of the Maxwell superalgebra sℳ4. We extend this result to all minimal Maxwell superalgebras type sℳ m + 2. The invariance under supersymmetry transformations is also analized.

Maxwell superalgebras and Abelian semigroup expansion

The Abelian semigroup expansion is a powerful and simple method to derive new Lie algebras from a given one. Recently it was shown that the S-expansion of so(3,2) leads us to the Maxwell algebra M. In this paper we extend this result to superalgebras, by proving that different choices of abelian semigroups S lead to interesting D=4 Maxwell Superalgebras. In particular, the minimal Maxwell superalgebra sM and the N-extended Maxwell superalgebra sM(N) recently found by the Maurer–Cartan expansion procedure, are derived alternatively as an S-expansion of osp(4|N). Moreover, we show that new minimal Maxwell superalgebras type sMm+2 and their N-extended generalization can be obtained using the S-expansion procedure.

M supergravity and abelian semigroups

A gauge theory for the M algebra in eleven-dimensional spacetime is put forward. The gauge-invariant Lagrangian corresponds to a transgression form. This class of Lagrangians modifies Chern-Simons theory with the addition of a regularizing boundary term.The M algebra-invariant tensor required to define the theory comes from regarding the algebra as an abelian semigroup expansion of the orthsymplectic algebra osp (32|1). The explicit form of the Lagrangian is found by means of a transgression-specific subspace separation method. Dynamical properties are briefly analyzed through an example. The equations of motion are found to place severe constraints on the geometry, which might be partially alleviated by allowing for nonzero torsion.

Construction of Lie algebras and invariant tensors through abelian semigroups

The Abelian Semigroup Expansion Method for Lie Algebras is briefly explained. Given a Lie Algebra and a discrete abelian semigroup, the method allows us to directly build new Lie Algebras with their corresponding non-trivial invariant tensors. The Method is especially interesting in the context of M-Theory, because it allows us to construct M-Algebra Invariant Chern-Simons/Transgression Lagrangians in d = 11.

Eleven-dimensional gauge theory for the M-algebra as an Abelian semigroup expansion of $\mathfrak{osp} ( 32 | 1 )$

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 $\mathfrak{osp}(32|1)$ 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.