Topological regularization and self-duality in four-dimensional anti-de Sitter gravity

Details Topological regularization and self-duality in four-dimensional anti-de Sitter gravity Topological regularization and self-duality in four-dimensional anti-de Sitter gravity

2009-02-12

arxiv.org/abs/0902.2082v2

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, no figures; enlarged discussion on self-duality condition for AAdS spacetimes, references added, final version for P

Scientific paper

It is shown that the addition of a topological invariant (Gauss-Bonnet term) to the anti-de Sitter (AdS) gravity action in four dimensions recovers the standard regularization given by holographic renormalization procedure. This crucial step makes possible the inclusion of an odd parity invariant (Pontryagin term) whose coupling is fixed by demanding an asymptotic (anti) self-dual condition on the Weyl tensor. This argument allows to find the dual point of the theory where the holographic stress tensor is related to the boundary Cotton tensor as $T_{j}^{i}=\pm (\ell ^{2}/8\pi G)C_{j}^{i}$, which has been observed in recent literature in solitonic solutions and hydrodynamic models. A general procedure to generate the counterterm series for AdS gravity in any even dimension from the corresponding Euler term is also briefly discussed.

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