Holographic renormalization of Horndeski gravity

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.

Magnetized AdS/BCFT Correspondence in Horndeski Gravity

“…Here, for  H , we have that R = g 𝜇𝜈 R 𝜇𝜈 , G 𝜇𝜈 and Λ represent the scalar curvature, the Einstein tensor, and the cosmological constant respectively, while that 𝜙 = 𝜙(r) is a scalar field, 𝛼, and 𝛾 are coupling constants. It is interesting to note that Lagrangian (2) has been explored from the point of view of hairy BH configurations, [30,[58][59][60][61] boson and neutron stars, [62][63][64] Hairy Taub-NUT/Bolt-AdS solutions, [65] holographic renormalization, [66] as well as holographic applications such that quantum complexity and shear viscosity. [31,32,34,40,67]  M represents the Maxwell Lagrangian, where F 𝜇𝜈 = 𝜕 𝜇 A 𝜈 − 𝜕 𝜈 A 𝜇 and e is a coupling constant.…”