Generalized Poincare algebras and Lovelock-Cartan gravity theory

TL;DR

This paper reformulates Lovelock-Cartan gravity as a unifying framework that connects General Relativity, Chern-Simons, and Born-Infeld theories through generalized Poincaré algebras, highlighting the role of torsion.

Contribution

It introduces a new formulation of Lovelock-Cartan gravity using generalized Poincaré algebras, unifying different gravity theories and incorporating torsion explicitly.

Findings

Lagrangian reduces to General Relativity in a specific limit.

In odd dimensions, it yields a Chern-Simons theory invariant under $rak{B}_{2n+1}$.

In even dimensions, it results in a Born-Infeld theory under a subalgebra.

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 Poincar\'{e} 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.