  Heavy-heavy-light-light (HHLL) correlators of pairwise identical scalars in
CFTs with a large central charge in any number of dimensions admit a double
scaling limit where the ratio of the heavy conformal dimension to the central
charge becomes large as the separation between the light operators becomes
null. In this limit the stress tensor sector of a generic HHLL correlator
receives contributions from the multi stress tensor operators with any number
of stress tensors, as long as their twist is not increased by index
contractions. We show how one can compute this leading twist stress tensor
sector when the conformal dimension of the light operators is large and the
stress tensor sector approximates the thermal CFT correlator. In this regime
the value of the correlator is related to the length of the spacelike geodesic
which approaches the boundary of the dual asymptotically AdS spacetime at the
points of light operator insertions. We provide a detailed description of the
infinite volume limit. In two spacetime dimensions the HHLL Virasoro vacuum
block is reproduced, while in four spacetime dimensions the result is written
in terms of elliptic integrals.
