Holographic renormalization of Horndeski gravity

TL;DR

This paper investigates the holographic renormalization of a sector of Horndeski gravity involving scalar couplings to curvature terms, deriving conditions for finiteness, boundary terms, and physical constraints.

Contribution

It provides a detailed analysis of the renormalization process for scalar-curvature couplings in Horndeski gravity, including boundary terms and holographic correlators.

Findings

Finite action and charges achieved with specific boundary terms

Effective scalar mass modifies the Breitenlohner-Freedman bound

Constraints on parameters from boundary scaling symmetry

Abstract

We study the renormalization of a particular sector of Horndeski theory. In particular, we focus on the nonminimal coupling of a scalar field to the Gauss-Bonnet term and its kinetic coupling to the Einstein tensor. Adopting a power expansion on the scalar function that couples the Gauss-Bonnet term, we find specific conditions on their coefficients such that the action and charges are finite. To accomplish the latter, we add a finite set of intrinsic boundary terms. The contribution of the nonminimal coupling generates an effective scalar mass, allowing us to recover a modified Breitenlohner-Freedman bound. Furthermore, we compute the holographic 1-point functions and Ward identities associated with the scalar field and the metric. We constrain the parameter space of the theory by taking into account the preservation of scaling symmetry at the boundary.