Chern-Simons and Born-Infeld gravity theories and Maxwell algebras type

Abstract

Recently was shown that standard odd and even-dimensional General Relativity can be obtained from a $(2n+1)$-dimensional Chern-Simons Lagrangian invariant under the $B_{2n+1}$ algebra and from a $(2n)$-dimensional Born-Infeld Lagrangian invariant under a subalgebra ${\mathcal{L}}^{{\mathcal{B}}_{2n+1}}$ respectively. Very Recently, it was shown that the generalized Inönü-Wigner contraction of the generalized AdS-Maxwell algebras provides Maxwell algebras types ${\mathcal{M}}_m$ which correspond to the so called $B_m$ Lie algebras. In this article we report on a simple model that suggests a mechanism by which standard odd-dimensional General Relativity may emerge as a weak coupling constant limit of a $(2p+1)$-dimensional Chern-Simons Lagrangian invariant under the Maxwell algebra type ${\mathcal{M}}_{2m+1}$, if and only if $m\ge p$. Similarly, we show that standard even-dimensional General Relativity emerges as a weak coupling constant limit of a $(2p)$-dimensional Born-Infeld type Lagrangian invariant under a subalgebra ${\mathcal{L}}^{{\mathcal{M}}_{2m}}$ of the Maxwell algebra type, if and only if $m\ge p$. It is shown that when $m<p$ this is not possible for a $(2p+1)$-dimensional Chern-Simons Lagrangian invariant under the ${\mathcal{M}}_{2m+1}$ and for a $(2p)$-dimensional Born-Infeld type Lagrangian invariant under ${\mathcal{L}}^{{\mathcal{M}}_{2m}}$ algebra.

30 pages, accepted for publication in Eur.Phys.J.C. arXiv admin note: text overlap with arXiv:1309.0062

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• Expanding Lie (super)algebras through abelian semigroups

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