https://doi.org/10.1140/epjc/s10052-014-2741-6
Regular Article - Theoretical Physics
Chern–Simons and Born–Infeld gravity theories and Maxwell algebras type
Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción, Chile
* e-mail: pasalgad@udec.cl
Received:
27
August
2013
Accepted:
14
January
2014
Published online:
12
February
2014
Recently it was shown that standard odd- and even-dimensional general relativity can be obtained from a 
-dimensional Chern–Simons Lagrangian invariant under the 
algebra and from a 
-dimensional Born–Infeld Lagrangian invariant under a subalgebra 
, respectively. Very recently, it was shown that the generalized Inönü–Wigner contraction of the generalized AdS–Maxwell algebras provides Maxwell algebras of types 
which correspond to the so-called 
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 
-dimensional Chern–Simons Lagrangian invariant under the Maxwell algebra type 
, if and only if 
. Similarly, we show that standard even-dimensional general relativity emerges as the weak coupling constant limit of a 
-dimensional Born–Infeld type Lagrangian invariant under a subalgebra 
of the Maxwell algebra type, if and only if . It is shown that when 
this is not possible for a -dimensional Chern–Simons Lagrangian invariant under the and for a -dimensional Born–Infeld type Lagrangian invariant under the 
algebra.
© The Author(s), 2014
