Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-06-29
JHEP 0710:028,2007
Physics
High Energy Physics
High Energy Physics - Theory
26 pages, no figures; references added; version accepted for publication in JHEP
Scientific paper
10.1088/1126-6708/2007/10/028
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.
Miskovic Olivera
Olea Rodrigo
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