Chern-Simons Gravities Research Articles

Gravitational Chern–Simons, and Chern–Simons Gravity in All Dimensions

The construction of Chern–Simons gravities (CSG) and gravitational Chern–Simons densities (GCS) are considered. Since both these are definied $$via$$ the non-Abelian (nA) Chern–Simons densities (CS) in the appropriate representations, and the latter are defined only in odd dimensions, so are the CSG and the GCS. To overcome this restriction, it is proposed that instead of employing nA CS densities, the Higgs–CS (HCS) densities are employed, the latter being defined in all dimensions and hence leading to their gravitational counterparts, HCS-Gravity (HCSG) Lagrangians and gravitational-HCS (GHCS) densities, not all of them restricted to odd dimensions. A detailed definition for a GHCS density in 3 + 1 dimensions is presented, and, a new result in black hole solutions in CSG gravity models in all odd dimensions is presented.

A remark on black holes of Chern–Simons gravities in 2n + 1 dimensions: n = 1,2,3

A systematic prescription for constructing Chern–Simons gravities in all odd dimensions is given, and it is shown that Chern–Simons gravities in [Formula: see text] dimensions admit solutions described by the same lapse function which describes the BTZ black hole in the [Formula: see text] case. This has been carried out explicitly for [Formula: see text]. Moreover, it is seen that these solutions are unique.

Stringy (Galilei) Newton-Hooke Chern-Simons gravities

We construct Chern-Simons gravities in (2 + 1)-dimensional space-time considering the Stringy Galilei algebra both with and without non-central extensions. In the first case, there is an invariant and non-degenerate bilinear form, however the field equations do not allow to express the spin connections in terms of the dreibeins. In the second case there is no invariant non-degenerate bilinear form. Therefore, in both cases we do not have an ordinary gravity theory. Instead, if we consider the stringy Newton-Hooke algebra with extensions as gauge group we have an invariant non-degenerate metric and from the field equations we express the spin connections in terms of the geometric fields.

Chern–Simons Gravities (CSG) and Gravitational Chern–Simons (GCS) Densities in All Dimensions

Chern-Simons gravities and gravitational Chern-Simons densities are constructed using the non-Abelian Yang-Mills Chern-Simons densities. As such, they are defined only in odd dimensions. We propose instead an analogous construction employing what we term Higgs--Chern-Simons (HCS) densities, which are defined in $all\ dimensions$. This enables the definition of extended versions of Chern-Simons gravities in all dimensions. Employing the same prescription, the definition of gravitational Chern-Simons densities is extended to all even dimensions, but only to $4p-1$ $odd$ dimensions. All our considerations are restricted to $vacuum$ fields.

Gauge symmetries and holographic anomalies of Chern-Simons and transgression AdS gravity

We review the issue of gauge and gravitational anomalies with backgrounds, maybe offering a new outlook on some aspects of these questions. We compute the holographic anomalies of hypothetical theories dual, in the sense of the AdS-CFT correspondence, to Chern-Simons AdS gravities. Those anomalies are either gauge anomalies associated to the AdS gauge group of the theory or diffeomorphism anomalies, with each kind related to the other. As a result of using suitable action principles por Chern-Simons AdS gravities, coming from Transgression forms, we obtain finite results without the need for further regularization. Our results are of potential interest for Lovelock gravity theories, as it has been shown that the boundary terms dictated by the transgressions for Chern-Simons gravities are also suitable to regularize Lovelock theories. The Wess-Zumino consistency condition ensures that anomalies of the generic form computed here should appear for these and other theories.

Action principles for Transgression and Chern-Simons AdS gravities

Chern-Simons gravities are theories with a lagrangian given by a Chern-Simons form constructed from a space-time gauge group. In previous investigations we showed that, for some special field configurations that are solutions of the field equations, the extension from Chern-Simons to Transgression forms as lagrangians, motivated by gauge invariance, automatically yields the boundary terms required to regularize the theory, giving finite conserved charges and black hole thermodynamics. Further work by other researchers showed that one of the action functionals considered in the above mentioned work yields a well defined action principle in the metric (zero torsion) case and for asymptotically Anti de Sitter (AdS) space-times. In the present work we consider several action functionals for Chern-Simons AdS gravity constructed from Transgression forms, and show the action principles to be well defined and the Noether charges and Euclidean action to be finite for field configurations satisfying only that the gauge field curvature (field strength) for the AdS gauge group is asymptotically finite. For that purpose we consider an asymptotic expansion of the vielbein and spin connection that may be regarded as a perturbation of an AdS space-time, but allowing a non zero torsion. Our results are of potential interest for Lovelock gravity theories, as it has been shown that the boundary terms dictated by the transgressions for Chern-Simons gravities are also suitable to regularize Lovelock theories.

Couplings of gravitational currents with Chern-Simons gravities

The coupling of conserved p-brane currents with non-Abelian gaugetheories is done consistently by using Chern-Simons forms. Conserved currents localized on p-branes that have a gravitational origin can be constructed from Killing-Yano forms of the underlying spacetime. We propose a generalization of the coupling procedure with Chern-Simons gravities to the case of gravitational conserved currents. In odd dimensions, the field equations of coupled Chern-Simons gravities that describe the local curvature on p-branes are obtained. In special cases of three and five dimensions, the field equations are investigated in detail.

Couplings between Chern-Simons gravities and2p-branes

The interaction between Chern-Simons (CS) theories and localized external sources ($2p$-branes) is analyzed. This interaction generalizes the minimal coupling between a point charge (0-brane) and a gauge connection. The external currents that define the $2p$ branes are covariantly constant ($D\ensuremath{-}2p\ensuremath{-}1$)-forms coupled to ($2p\ensuremath{-}1$) CS forms. The general expression for the sources---charged with respect to the corresponding gauge algebra---is presented, focusing on two special cases: 0-branes and ($D\ensuremath{-}3$)-branes. In any dimension, 0-branes are constructed as topological defects produced by a surface deficit of ($D\ensuremath{-}2$)-sphere in anti-de Sitter space, and they are not constant curvature spaces for $D>3$. They correspond to dimensionally continued black holes with negative mass. On the other hand, in the case of CS (super) gravities, the ($D\ensuremath{-}3$)-branes are naked conical singularities (topological defects) obtained by identification of points with a Killing vector. In $2+1$ dimensions, extremal spinning branes of this type are Bogomol'nyi-Prasad-Sommerfield states. Stable ($D\ensuremath{-}3$)-branes are shown to exist also in higher dimensions, as well. Classical field equations are also discussed, and in the presence of sources there is a large number of inequivalent and disconnected sectors in solution space.

Einstein-Cartan formulation of Chern-Simons Lorentz-violating gravity

We consider a modification of the standard Einstein theory in four dimensions, alternative to R. Jackiw and S.-Y. Pi, Phys. Rev. D 68, 104012 (2003), since it is based on the first-order (Einstein-Cartan) approach to general relativity, whose gauge structure is manifest. This is done by introducing an additional topological term in the action which becomes a Lorentz-violating term by virtue of the dependence of the coupling on the space-time point. We obtain a condition on the solutions of the Einstein equations, such that they persist in the deformed theory, and show that the solutions remarkably correspond to the classical solutions of a collection of independent $2+1$-dimensional (topological) Chern-Simons gravities. Finally, we study the relation with the standard second-order approach and argue that they both coincide to leading order in the modulus of the Lorentz-violating vector field.