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

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• 作者：P. K. Concha (1)
  D. M. Pe?afiel (1)
  E. K. Rodriguez (1)
  P. Salgado (1)
  
• 刊名：The European Physical Journal C - Particles and Fields
• 出版年：2014
• 出版时间：February 2014
• 年：2014
• 卷：74
• 期：2
• 全文大小：479 KB
• 作者单位：P. K. Concha (1)
  D. M. Pe?afiel (1)
  E. K. Rodriguez (1)
  P. Salgado (1)
  
  1. Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción, Chile
  
• ISSN：1434-6052

文摘

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 In?nü–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.