  We study 2-point correlation functions for scalar operators in position space
through holography including bulk cubic couplings as well as higher curvature
couplings to the square of the Weyl tensor. We focus on scalar operators with
large conformal dimensions. This allows us to use the geodesic approximation
for propagators. In addition to the leading order contribution, captured by
geodesics anchored at the insertion points of the operators on the boundary and
probing the bulk geometry thoroughly studied in the literature, the first
correction is given by a Witten diagram involving both the bulk cubic coupling
and the higher curvature couplings. As a result, this correction is
proportional to the VEV of a neutral operator $O_k$ and thus probes the
interior of the black hole exactly as in the case studied by Grinberg and
Maldacena [13]. The form of the correction matches the general expectations in
CFT and allows to identify the contributions of $T^nO_k$ (being $T^n$ the
general contraction of n energy-momentum tensors) to the 2-point function. This
correction is actually the leading term for off-diagonal correlators (i.e.
correlators for operators of different conformal dimension), which can then be
computed holographically in this way.
