An identity in Riemann–Cartan geometry

Nieh, H. T.; Yan, Mu‐Lin

doi:10.1063/1.525379

Cited by 267 publications

(308 citation statements)

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“…In CS supergravity there is a non-minimal coupling between geometry and the electromagnetic field brought about by the symmetric invariant tensor component g 1ab , L int = α 2 R ab R ab + 2 ℓ 2 R ab e a e b − T a T a A , (2.8) where R ab R ab is the Lorentz Pontryagin four-form and T a T a − R ab e a e b = d (T a e a ) is the Nieh-Yan invariant [16]. These define two topological invariants in four-dimensional Einstein-Cartan geometry, and the combination of both is the AdS Pontryagin fourform [17].…”

Section: Jhep08(2014)083mentioning

confidence: 99%

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Black hole solutions in Chern-Simons AdS supergravity

Giribet

Merino

Mišković

et al. 2014

J. High Energ. Phys.

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We study charged AdS black hole solutions in five-dimensional Chern-Simons supergravity. The minimal supergroup containing such AdS 5 × U(1) configurations is the superunitary group SU(2, 2|N ). For this model, we find analytic black hole solutions that asymptote to locally AdS 5 spacetime at the boundary. A solution can carry U(1) charge provided the spacetime torsion is non-vanishing. Thus, we analyze the most general configuration consistent with the local AdS 5 isometries in Riemann-Cartan space. The coupling of torsion in the action resembles that of the universal axion of string theory, and it is ultimately due to this field that the theory acquires propagating degrees of freedom. Through a careful analysis of the canonical structure the local degrees of freedom of the theory are identified in the static symmetric sector of phase space.

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Section: Jhep08(2014)083mentioning

confidence: 99%

“…The field equations that extremize this action with respect to the metric are 16) where the contribution of the quadratic terms in curvature is given by the Lanczos tensor,…”

Section: Jhep08(2014)083mentioning

confidence: 99%

Black hole solutions in Chern-Simons AdS supergravity

Giribet

Merino

Mišković

et al. 2014

J. High Energ. Phys.

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“…This option, however, depends on the spacetime dimension. For instance, in four dimensions (n 4) we can consider a 3-parameter family of boundary forms These 3-forms correspond to the Nieh-Yan [50,51], the Pontryagin, and the Euler topological invariants, respectively. They represent the so-called gravitational (translational and rotational) Chern-Simons 3-forms, see [52] for more details.…”

Section: Relocalization Of the Currentsmentioning

confidence: 99%

Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry

2006

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We discuss conservation laws for gravity theories invariant under general coordinate and local Lorentz transformations. We demonstrate the possibility to formulate these conservation laws in many covariant and noncovariant(ly looking) ways. An interesting mathematical fact underlies such a diversity: there is a certain ambiguity in a definition of the (Lorentz-) covariant generalization of the usual Lie derivative. Using this freedom, we develop a general approach to the construction of invariant conserved currents generated by an arbitrary vector field on the spacetime. This is done in any dimension, for any Lagrangian of the gravitational field and of a (minimally or nonminimally) coupled matter field. A development of the ''regularization via relocalization'' scheme is used to obtain finite conserved quantities for asymptotically nonflat solutions. We illustrate how our formalism works by some explicit examples.

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“…Up to normalizations, the four-forms (26) and (27) are known as Nieh-Yan [52] and gravitational Pontrjagin term, respectively. On the other hand, the topological Euler term…”

Section: Appendix A: Riemann-cartan Geometry In Clifford Algebra-valumentioning

confidence: 99%

Einsteinian gravity from a topological action

Mielke

2008

Gen Relativ Gravit

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Abstract.The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature as classical instanton type background.However, exact vacuum solutions with double duality properties exhibit a 'vacuum degeneracy'. By modifying the duality via a scale breaking term, we demonstrate that only Einstein's equations with an induced cosmological constant emerge for the topology of the macroscopic background. This may have repercussions on the problem of 'dark energy' as well as 'dark matter' modeled by a torsion induced quintaxion.

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An identity in Riemann–Cartan geometry

Abstract: We derive a new Gauss–Bonnet type identity in Riemann-Cartan geometry: (−g)1/2εμνλρ (Rμνλρ + (1/2) CαμνCαλν) = ∂μ (−(−g)1/2εμνλρCμνλρ), where Cαμν is the torsion tensor.

Cited by 267 publications

References 1 publication

Black hole solutions in Chern-Simons AdS supergravity

Black hole solutions in Chern-Simons AdS supergravity

Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry

Einsteinian gravity from a topological action

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