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

Recently it 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 $${\mathcal {L}}^{B_{2n+1}}$$ , respectively. Very recently, it was shown that the generalized Inönü–Wigner contraction of the generalized AdS–Maxwell algebras provides Maxwell algebras of 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 the 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 the weak coupling constant limit of a $$(2p)$$ -dimensional Born–Infeld type Lagrangian invariant under a subalgebra $${\mathcal {L}}^{{\mathcal {M}}_{\mathbf {2m}}}$$ 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 the $${\mathcal {L}}^{{\mathcal {M}} _{\mathbf {2m}}}$$ algebra.

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