Conformal blocks in 2D Carrollian-Galilean CFTs and excited state entanglement entropy

We advance the study of flat space holography by computing the entanglement entropy of highly excited states in two-dimensional Carrollian/Galilean Conformal Field Theories ( C / G CFTs). Our approach is centered on a novel, physically intuitive derivation of the heavy-light conformal block in the large central charge limit, where the backreaction of heavy operators is absorbed by a C / G conformal coordinate transformation. Using this result and the replica trick, we find that the entanglement entropy of highly excited states assumes a thermal form, providing a concrete realization of the eigenstate thermalization hypothesis. This field-theoretic result perfectly reproduces the holographic entanglement entropy computed via the swing surface proposal in three-dimensional Einstein gravity, for backgrounds corresponding to spinning particles and flat space cosmological solutions. This agreement establishes a precise dictionary relating the weight Δ and charge ξ of the boundary state to the mass m and angular momentum j of the dual spacetime, offering a powerful consistency check for the Flat/Carrollian conformal field theory correspondence.