Semi-classical BMS-blocks from the Oscillator Construction

Flat-space holography requires a thorough understanding of BMS symmetry. We introduce an oscillator construction of the highest-weight representation of the $\mathfrak{bms}_3$ algebra and show that it is consistent with known results concerning the $\mathfrak{bms}_3$ module. We take advantage of this framework to prove that $\mathfrak{bms}_3$-blocks exponentiate in the semi-classical limit, where one of the central charges is large. Within this context, we compute perturbatively heavy, and heavy-light vacuum $\mathfrak{bms}_3$-blocks.