Semi-classical BMS$_3$ blocks and flat holography

We present the construction of BMS$_3$ blocks in a two-dimensional field theory and compare the results with holographic computations involving probe particles propagating in flat space cosmologies. On the field theory side, we generalize the monodromy method used in the context of AdS/CFT to theories with BMS symmetry. On the bulk side we consider geodesic Feynman diagrams, recently introduced in [arXiv:1712.07131], evaluated in locally flat geometries generated by backreaction of heavy BMS primary operators. We comment on the implications of these results for the eigenstate thermalization hypothesis in flat holography.