  Correlators in conformal field theory are naturally organized as a sum over
conformal blocks. In holographic theories, this sum must reorganize into a path
integral over bulk fields and geometries. We explore how these two sums are
related in the case of a point particle moving in the background of a 3d
collapsing black hole. The conformal block expansion is recast as a sum over
paths of the first-quantized particle moving in the bulk geometry. Off-shell
worldlines of the particle correspond to subdominant contributions in the
Euclidean conformal block expansion, but these same operators must be included
in order to correctly reproduce complex saddles in the Lorentzian theory.
During thermalization, a complex saddle dominates under certain circumstances;
in this case, the CFT correlator is not given by the Virasoro identity block in
any channel, but can be recovered by summing heavy operators. This effectively
converts the conformal block expansion in CFT from a sum over intermediate
states to a sum over channels that mimics the bulk path integral.
