"Topological invariants, Kounterterms and self-duality in four-dimensional 
anti-de Sitter gravity." 

Abstract: 

The AdS/CFT correspondence conjectures a profound relation between 
gravity with negative cosmological constant defined in a spacetime and a 
Conformal Field Theory living on its boundary. 
In order to realize this duality, it is necessary to extract the finite 
information contained in the action (and in the boundary stress tensor 
derived from it) by means of a procedure known as holographic 
renormalization. This results in the addition to the bulk action of 
intrinsic counterterms which cancel out the divergences in the 
asymptotic region. 

As an alternative to the above method, counterterterms with dependence on 
the extrinsic curvature of the boundary (also known as Kounterterms) have 
been proposed. In any $D=2n$ dimension, they are simply given by the 
boundary term which appears in the 2n-dimensional Euler theorem and, 
therefore, they are connected to the existence of topological invariants 
in that dimension. 

In this seminar, we show how this "topological" regularization 
prescription generates the standard counterterm series by a suitable 
expansion of the fields. In particular, in four dimensions, adding the 
Gauss-Bonnet term to the action with a suitable coupling constant is 
equivalent to Balasubramanian-Kraus construction. This also opens 
the possibility of adding another topological invariant (Pontryagin term) 
to the action and fixing its coupling constant by taking a self-duality 
condition on the Weyl tensor. This argument provides a simple derivation 
of the holographic stress tensor/Cotton tensor duality recently noticed in 
the literature for soliton solutions and hydrodynamic models in AdS_4.