Renormalization of Einstein-Gauss-Bonnet AdS gravity

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.

💡 Research Summary

The paper presents a comprehensive holographic renormalization of Einstein‑Gauss‑Bonnet (EGB) gravity with a negative cosmological constant, focusing on asymptotically AdS spacetimes in arbitrary dimensions up to seven. The authors begin by reviewing the role of higher‑curvature corrections in string theory and AdS/CFT, emphasizing that the Gauss‑Bonnet term introduces a new coupling α that modifies the effective AdS radius ℓ_eff and leads to two distinct maximally symmetric vacua. They discuss the degenerate point where the two vacua coalesce, which will be relevant for special cases later.

In Section 2 the bulk action I_EGB = κ∫√−g(R−2Λ+α G) is introduced, with G the Gauss‑Bonnet invariant. Varying the action yields second‑order field equations E_{μν}=G_{μν}+α H_{μν}=0, where H_{μν} is the Lanczos tensor. Solving the algebraic relation for ℓ_eff gives two possible effective radii ℓ_eff⁺ and ℓ_eff⁻, each defining a different vacuum branch. The authors then adopt the Fefferman‑Graham (FG) gauge, \