Semi-classical BMS-blocks from the Oscillator Construction

TL;DR

This paper develops an oscillator-based framework for $ms_3$ algebra representations, demonstrating that $ms_3$-blocks exponentiate semi-classically and computing specific vacuum blocks, advancing flat-space holography understanding.

Contribution

It introduces a novel oscillator construction for $ms_3$ modules and proves the semi-classical exponentiation of $ms_3$-blocks, providing new computational tools.

Findings

$ms_3$-blocks exponentiate in the semi-classical limit.

Constructed consistent highest-weight $ms_3$ modules using oscillators.

Computed perturbative heavy and heavy-light vacuum $ms_3$-blocks.

Abstract

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.