Renormalization of Einstein-Gauss-Bonnet AdS gravity

TL;DR

This paper develops and cross-validates holographic renormalization for Einstein-Gauss-Bonnet AdS gravity in arbitrary dimensions, including a fully covariant 6D scheme based on conformal invariants. It shows that the standard holographic renormalization and the conformal-invariant covariant approach produce identical holographic stress tensors and finite charges, and applies these methods to six-dimensional topological BD black holes with nontrivial boundary conformal structure. The study derives explicit counterterms up to fourth derivative order, analyzes the role of Weyl, Schouten, Cotton, and Bach tensors, and demonstrates that BD black holes respect proper thermodynamics with corrected entropy and a well-defined first law. The results have implications for holographic entanglement, quantum information measures, and the broader understanding of higher-curvature gravity in the AdS/CFT context.

Abstract

The asymptotic analysis for the metric of a generic solution of Einstein-Gauss-Bonnet AdS theory is provided by solving the field equations in the Fefferman-Graham frame. Using standard holographic renormalization, the counterterms that render the action finite are found up to seven spacetime dimensions. In the case of 6D, an equivalent formulation that permits a fully covariant determination of the counterterms is introduced, based on the finiteness of conformal invariants. It is shown that both schemes end up in the same holographic stress-energy tensor. Physical properties of six-dimensional topological Boulware-Deser black holes in Einstein-Gauss-Bonnet-AdS$_6$ gravity, whose boundary has nontrivial conformal features, are worked out in detail. Employing both renormalization prescriptions, finite asymptotic charges are found, and the correct black hole thermodynamics is recovered.