Einstein–Hilbert action with cosmological term from Chern–Simons gravity

González, Nelson; Salgado, P.; Rubio, Gustavo; Salgado, S.

doi:10.1016/j.geomphys.2014.08.013

Cited by 20 publications

(35 citation statements)

References 17 publications

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“…But our result enters in contradiction with [18], where the theory is claimed to depend on four independent coupling constants. The consequence of our result is to invalidate the C5 symmetry of the Einstein-Hilbert model presented in Section 8 of [18]. action term, a cosmological term and a term quadratic in the curvature, of the Gauss-Bonnet type.…”

Section: Introductioncontrasting

confidence: 99%

“…Our first result concerns a fact about the algebra C 5 defined as the expansion of the 5D (anti-)de Sitter by the reduced group S whose multplication table is displayed in Table 1: we have shown that there are two independent symmetric invariant tensors of rank 3 in its adjoint representation, given by the equation (3.16), instead of four as claimed by the authors of [18], who consider the same gauge group. This result provides indeed a counter-example to the Theorem 2 in Section 5 of [18].…”

Section: Discussionmentioning

confidence: 72%

“…The geometric part of the action, obtained by taking B = 0, is identical to the (a)ds 5 one, as originally given in [5] and summarized in Section 2. When written in terms of the 5-bein e and the 5D Lorentz connection ω (see (2.11)), the latter action shows, beyond the Einstein-Hilbert and cosmological terms a Gauss-Bonnet type term present which cannot be eliminated by any choice of the coupling constants -in contradiction with the result of [18].…”

Section: Discussionmentioning

confidence: 96%

“…where the 3-selector [18] S ijk l is defined by and c 0 and c 1 are two arbitrary constants. So, the most general action is an arbitrary linear combination of two invariant actions 8 .…”

Section: Invariant Tensorsmentioning

confidence: 99%

“…This enables the introduction of new fields in the theory beyond the gravitation field. In particular, it was claimed in [18] that, using an alternative expansion process called "H-reduction" leading to a symmetry algebra called C 5 , it was possible to obtain a theory that reproduces exactly GR coupled with some matter fields, so that it would be a good candidate for the purpose of obtaining a quantum theory for gravitation consistent with Einstein's theory 1 .…”

Section: Introductionmentioning

confidence: 99%

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Five dimensional Chern–Simons gravity for the expanded (anti)-de Sitter gauge group $${\hbox {C}}_5$$

Piguet

2020

Eur. Phys. J. C

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We study the Hamiltonian dynamics of a five-dimensional Chern-Simons theory for the gauge algebra C 5 of Izaurieta, Rodriguez and Salgado, the so-called S H -expansão of the 5D (anti-)de Sitter algebra (a)ds, based on the cyclic group Z 4 . The theory consists of a 1-form field containing the (a)ds gravitation variables and 1-form field transforming in the adjoint representation of (a)ds. The gravitational part of the action necessarily contains a term quadratic in the curvature, beyond the Einstein-Hilbert and cosmological terms, for any choice of the two independent coupling constants. The total action is also invariant under a new local symmetry, called "crossed diffeomorphisms", beyond the usual space-time diffeomorphisms. The number of physical degrees of freedom is computed. The theory is shown to be "generic" in the sense of Bañados, Garay and Henneaux, i.e., the constraint associated to the time diffeomorphisms is not independent from the other constraints.

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Section: Introductioncontrasting

confidence: 99%

Section: Discussionmentioning

confidence: 72%

Section: Discussionmentioning

confidence: 96%

“…where the 3-selector [18] S ijk l is defined by and c 0 and c 1 are two arbitrary constants. So, the most general action is an arbitrary linear combination of two invariant actions 8 .…”

Section: Invariant Tensorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Five dimensional Chern–Simons gravity for the expanded (anti)-de Sitter gauge group $${\hbox {C}}_5$$

Piguet

2020

Eur. Phys. J. C

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An analytic method forS-Expansion involving resonance and reduction

et al. 2016

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In this paper we describe an analytic method able to give the multiplication table(s) of the set(s) involved in an S-expansion process (with either resonance or 0 S -resonant-reduction) for reaching a target Lie (super)algebra from a starting one, after having properly chosen the partitions over subspaces of the considered (super)algebras.This analytic method gives us a simple set of expressions to find the subset decomposition of the set(s) involved in the process. Then, we use the information coming from both the initial (super)algebra and the target one for reaching the multiplication table(s) of the mentioned set(s). Finally, we check associativity with an auxiliary computational algorithm, in order to understand whether the obtained set(s) can describe semigroup(s) or just abelian set(s) connecting two (super)algebras.We also give some interesting examples of application, which check and corroborate our analytic procedure and also generalize some result already presented in the literature. * marcalderon@udec.cl †

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On the hidden maxwell superalgebra underlying supergravity

Peñafiel

Ravera

2017

Fortschritte der Physik

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In this work, we expand the hidden AdS-Lorentz superalgebra underlying D = 4 supergravity, reaching a (hidden) Maxwell superalgebra. The latter can be viewed as an extension involving cosmological constant of the superalgebra underlying D = 4 supergravity in flat spacetime. We write the Maurer-Cartan equations in this context and we find some interesting extensions of the antisymmetric 3-form A (3) appearing in the Free Differential Algebra in Minkowski space. The structure of Free Differential Algebras is obtained by considering the zero curvature equations. We write the parametrization of A (3) in terms of 1-forms and we rend the topological features of its extensions manifest. We interestingly find out that the structure of these extensions, and consequently the structure of the corresponding boundary contribution dA (3) , strongly depends on the form of the extra fermionic generator appearing in the hidden Maxwell superalgebra. The model we develop in this work is defined in an enlarged superspace with respect to the ordinary one, and the extra bosonic and fermionic 1-forms required for the closure of the hidden Maxwell superalgebra must be considered as physical fields in this enlarged superspace. * diegomolina@udec.cl †

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Einstein–Hilbert action with cosmological term from Chern–Simons gravity

Cited by 20 publications

References 17 publications

Five dimensional Chern–Simons gravity for the expanded (anti)-de Sitter gauge group $${\hbox {C}}_5$$

Five dimensional Chern–Simons gravity for the expanded (anti)-de Sitter gauge group $${\hbox {C}}_5$$

An analytic method forS-Expansion involving resonance and reduction

On the hidden maxwell superalgebra underlying supergravity

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