Holographic correlation functions in Critical Gravity

TL;DR

This paper calculates the holographic stress tensor and energy-momentum tensor in critical Einstein-Weyl gravity, revealing the role of non-Einstein modes and logarithmic terms through a specific renormalization scheme.

Contribution

It introduces a renormalization scheme using a Gauss-Bonnet term that cancels Einstein modes, highlighting the significance of non-Einstein modes in holographic correlators.

Findings

All Einstein modes are canceled by the renormalization scheme.

Non-Einstein modes associated with logarithmic terms are characterized by the Bach tensor.

Explicit holographic 1-point functions are computed for generic boundary sources.

Abstract

We compute the holographic stress tensor and the logarithmic energy-momentum tensor of Einstein-Weyl gravity at the critical point. This computation is carried out performing a holographic expansion in a bulk action supplemented by the Gauss-Bonnet term with a fixed coupling. The renormalization scheme defined by the addition of this topological term has the remarkable feature that all Einstein modes are identically cancelled both from the action and its variation. Thus, what remains comes from a nonvanishing Bach tensor, which accounts for non-Einstein modes associated to logarithmic terms which appear in the expansion of the metric. In particular, we compute the holographic $1$-point functions for a generic boundary geometric source.