### Resumen

We revise two regularization mechanisms for Lovelock gravity with AdS asymptotics. The first one corresponds to the Dirichlet counterterm method, where local functionals of the boundary metric are added to the bulk action on top of a Gibbons-Hawking-Myers term that defines the Dirichlet problem in gravity. The generalized Gibbons-Hawking term can be found in any Lovelock theory following the Myers' procedure to achieve a well-posed action principle for a Dirichlet boundary condition on the metric, which is proved to be equivalent to the Hamiltonian formulation for a radial foliation of spacetime. In turn, a closed expression for the Dirichlet counterterms does not exist for a generic Lovelock gravity. The second method supplements the bulk action with boundary terms which depend on the extrinsic curvature (Kounterterms), and whose explicit form is independent of the particular theory considered. In this paper, we use Dimensionally Continued AdS Gravity (Chern-Simons-AdS in odd and Born-Infeld-AdS in even dimensions) as a toy model to perform the first explicit comparison between both regularization prescriptions. This can be done thanks to the fact that, in this theory, the Dirichlet counterterms can be readily integrated out from the divergent part of the Dirichlet variation of the action. The agreement between both procedures at the level of the boundary terms suggests the existence of a general property of any Lovelock-AdS gravity: intrinsic counterterms are generated as the difference between the Kounterterm series and the corresponding Gibbons-Hawking-Myers term.

Idioma original | English |
---|---|

Número de artículo | 028 |

Publicación | Journal of High Energy Physics |

Volumen | 2007 |

N.º | 10 |

DOI | |

Estado | Published - 1 oct 2007 |

### Huella dactilar

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Citar esto

*Journal of High Energy Physics*,

*2007*(10), [028]. https://doi.org/10.1088/1126-6708/2007/10/028

}

*Journal of High Energy Physics*, vol. 2007, n.º 10, 028. https://doi.org/10.1088/1126-6708/2007/10/028

**Counterterms in dimensionally continued AdS gravity.** / Miković, Olivera; Olea, Rodrigo.

Resultado de la investigación: Article

TY - JOUR

T1 - Counterterms in dimensionally continued AdS gravity

AU - Miković, Olivera

AU - Olea, Rodrigo

PY - 2007/10/1

Y1 - 2007/10/1

N2 - We revise two regularization mechanisms for Lovelock gravity with AdS asymptotics. The first one corresponds to the Dirichlet counterterm method, where local functionals of the boundary metric are added to the bulk action on top of a Gibbons-Hawking-Myers term that defines the Dirichlet problem in gravity. The generalized Gibbons-Hawking term can be found in any Lovelock theory following the Myers' procedure to achieve a well-posed action principle for a Dirichlet boundary condition on the metric, which is proved to be equivalent to the Hamiltonian formulation for a radial foliation of spacetime. In turn, a closed expression for the Dirichlet counterterms does not exist for a generic Lovelock gravity. The second method supplements the bulk action with boundary terms which depend on the extrinsic curvature (Kounterterms), and whose explicit form is independent of the particular theory considered. In this paper, we use Dimensionally Continued AdS Gravity (Chern-Simons-AdS in odd and Born-Infeld-AdS in even dimensions) as a toy model to perform the first explicit comparison between both regularization prescriptions. This can be done thanks to the fact that, in this theory, the Dirichlet counterterms can be readily integrated out from the divergent part of the Dirichlet variation of the action. The agreement between both procedures at the level of the boundary terms suggests the existence of a general property of any Lovelock-AdS gravity: intrinsic counterterms are generated as the difference between the Kounterterm series and the corresponding Gibbons-Hawking-Myers term.

AB - We revise two regularization mechanisms for Lovelock gravity with AdS asymptotics. The first one corresponds to the Dirichlet counterterm method, where local functionals of the boundary metric are added to the bulk action on top of a Gibbons-Hawking-Myers term that defines the Dirichlet problem in gravity. The generalized Gibbons-Hawking term can be found in any Lovelock theory following the Myers' procedure to achieve a well-posed action principle for a Dirichlet boundary condition on the metric, which is proved to be equivalent to the Hamiltonian formulation for a radial foliation of spacetime. In turn, a closed expression for the Dirichlet counterterms does not exist for a generic Lovelock gravity. The second method supplements the bulk action with boundary terms which depend on the extrinsic curvature (Kounterterms), and whose explicit form is independent of the particular theory considered. In this paper, we use Dimensionally Continued AdS Gravity (Chern-Simons-AdS in odd and Born-Infeld-AdS in even dimensions) as a toy model to perform the first explicit comparison between both regularization prescriptions. This can be done thanks to the fact that, in this theory, the Dirichlet counterterms can be readily integrated out from the divergent part of the Dirichlet variation of the action. The agreement between both procedures at the level of the boundary terms suggests the existence of a general property of any Lovelock-AdS gravity: intrinsic counterterms are generated as the difference between the Kounterterm series and the corresponding Gibbons-Hawking-Myers term.

KW - Renormalization group

KW - Space-time symmetries

UR - http://www.scopus.com/inward/record.url?scp=35748937045&partnerID=8YFLogxK

U2 - 10.1088/1126-6708/2007/10/028

DO - 10.1088/1126-6708/2007/10/028

M3 - Article

VL - 2007

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 10

M1 - 028

ER -