Entanglement entropy in cubic gravitational theories

We derive the holographic entanglement entropy functional for a generic gravitational theory whose action contains terms up to cubic order in the Riemann tensor, and in any dimension. This is the simplest case for which the so-called splitting problem manifests itself, and we explicitly show that the two common splittings present in the literature - minimal and non-minimal - produce different functionals. We apply our results to the particular examples of a boundary disk and a boundary strip in a state dual to 4-dimensional Poincar\'e AdS in Einsteinian Cubic Gravity, obtaining the bulk entanglement surface for both functionals and finding that causal wedge inclusion is respected for both splittings and a wide range of values of the cubic coupling.