  We discuss correlators of light fields in heavy states in 3d gravity and
holographic 2d CFTs. In the bulk, the propagator of free fields in AdS
backgrounds containing a conical defect or a BTZ black hole can be obtained by
solving the wave equation, as well as by the method of images. On the boundary,
these geometries are sourced by heavy operator insertions, and the propagator
is dual to a heavy-light (HHLL) correlator. By matching its expansion in
Virasoro blocks to our bulk results, we determine the OPE coefficients of all
contributing states in both the s and t channels. In the s channel, these
states are excitations of the light field on top of the heavy state, and their
OPE coefficients are the amplitudes to create them. The t-channel OPE is
dominated by the Virasoro vacuum block, but there is also an infinite family of
light two-particle states that contribute to the correlator. The OPE
coefficients that couple these states to heavy operators represent their
expectation values in heavy backgrounds. We determine them exactly, derive
their asymptotic form at large twist, and discuss their behavior near and above
the BTZ threshold, where they become thermal one-point functions.
