Generalized Poincare algebras and Lovelock-Cartan gravity theory

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 Poincaré 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.

arXiv commentv2: 18 pages, minor modification in the title, some clarifications in the abstract, introduction and section 2, section 4 has been rewritten, typos corrected, references added. Accepted for publication in Physic letters B

References in corpus (10)

• Dimensionally Continued Black Holes
• Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity
• Expanding Lie (super)algebras through abelian semigroups
• Standard General Relativity from Chern-Simons Gravity
• Wess-Zumino term for the AdS superstring and generalized Inonu-Wigner contraction
• Higher Dimensional Gravity, Propagating Torsion and AdS Gauge Invariance
• Even-dimensional General Relativity from Born-Infeld gravity
• Chern-Simons and Born-Infeld gravity theories and Maxwell algebras type
• Extensions, expansions, Lie algebra cohomology and enlarged superspaces
• Dual Formulation of the Lie Algebra S-expansion Procedure

Cited by in corpus (37)

• N=1 Supergravity and Maxwell superalgebras
• Pure Lovelock gravity and Chern-Simons theory
• Generalized Chern-Simons higher-spin gravity theories in three dimensions
• On the Maxwell supergravity and flat limit in 2+1 dimensions
• Generalizing the ${\mathfrak{bms}}_3$ and 2D-conformal algebras by expanding the Virasoro algebra
• Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra
• Chern-Simons Supergravity in D=3 and Maxwell superalgebra
• New family of Maxwell like algebras
• On the Hidden Maxwell Superalgebra underlying D=4 Supergravity
• Three-dimensional Maxwellian extended Bargmann supergravity
• Lovelock gravities from Born-Infeld gravity theory
• Generalized Pure Lovelock Gravity
• $\mathcal{N}$-extended Maxwell supergravities as Chern-Simons theories in three spacetime dimensions
• Non-relativistic three-dimensional supergravity theories and semigroup expansion method
• Generalized supersymmetric cosmological term in N=1 Supergravity
• Inönü-Wigner Contraction and $D=2+1$ Supergravity
• On the supersymmetry invariance of flat supergravity with boundary
• Three-dimensional Poincaré supergravity and $\mathcal{N}$-extended supersymmetric BMS${}_3$ algebra
• Generalized Maxwellian exotic Bargmann gravity theory in three spacetime dimensions
• On the Supersymmetric Extension of Gauss-Bonnet like Gravity
• On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions
• Semi-simple enlargement of the ${\mathfrak{bms}}_3$ algebra from a $\mathfrak{so}(2,2)\oplus \mathfrak{so}(2,1)$ Chern-Simons theory
• Three-dimensional Maxwellian Extended Newtonian gravity and flat limit
• Generalized cosmological term in D=4 supergravity from a new AdS-Lorentz superalgebra
• Asymptotic Symmetries of Maxwell Chern-Simons Gravity with Torsion
• An Analytic Method for $S$-Expansion involving Resonance and Reduction
• Infinite S-Expansion with Ideal Subtraction and Some Applications
• Generalized AdS-Lorentz deformed supergravity on a manifold with boundary
• The Maxwell group in 2+1 dimensions and its infinite-dimensional enhancements
• On Stabilization of Maxwell-BMS Algebra
• Resonant superalgebras and $\mathcal{N}=1$ supergravity theories in three spacetime dimensions
• Deformation of Asymptotic Symmetry Algebras and Their Physical Realizations
• On a Java library to perform S-expansions of Lie algebras
• A free Lie algebra approach to curvature corrections to flat space-time
• A Java library to perform S-expansions of Lie algebras
• Scalar-tensor theory with EGB term from Einstein Chern-Simons gravity
• Generalization of extended Lie algebras by expansions of extended de Sitter algebra, in four-dimensions