Generalized Poincare algebras and Lovelock-Cartan gravity theory

Abstract

We show that the Lagrangian for Lovelock-Cartan gravity theory can be re-formulated as an action which leads to General Relativity in a certain limit. In odd dimensions the Lagrangian leads to a Chern-Simons theory invariant under the generalized Poincaré algebra ${\mathfrak{B}}_{2n+1},$ while in even dimensions the Lagrangian leads to a Born-Infeld theory invariant under a subalgebra of the ${\mathfrak{B}}_{2n+1}$ algebra. It is also shown that torsion may occur explicitly in the Lagrangian leading to new torsional Lagrangians, which are related to the Chern-Pontryagin character for the $B_{2n+1}$ group.

v2: 18 pages, minor modification in the title, some clarifications in the abstract, introduction and section 2, section 4 has been rewritten, typos corrected, references added. Accepted for publication in Physic letters B

References in corpus (1)

• Expanding Lie (super)algebras through abelian semigroups

Cited by in corpus (11)

• N=1 Supergravity and Maxwell superalgebras
• Generalized Pure Lovelock Gravity
• $\mathcal{N}$-extended Maxwell supergravities as Chern-Simons theories in three spacetime dimensions
• Non-relativistic three-dimensional supergravity theories and semigroup expansion method
• Inönü-Wigner Contraction and $D=2+1$ Supergravity
• On the Supersymmetric Extension of Gauss-Bonnet like Gravity
• An Analytic Method for $S$-Expansion involving Resonance and Reduction
• Resonant superalgebras and $\mathcal{N}=1$ supergravity theories in three spacetime dimensions
• Deformation of Asymptotic Symmetry Algebras and Their Physical Realizations
• Scalar-tensor theory with EGB term from Einstein Chern-Simons gravity
• Generalization of extended Lie algebras by expansions of extended de Sitter algebra, in four-dimensions