ar X iv : 0 90 2 . 20 82 v 1 [ he p - th ] 1 2 Fe b 20 09 Topological regularization and self - duality in four - dimensional anti - de Sitter gravity

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 provides a simple derivation of the holographic stress tensor/Cotton tensor duality 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.