Free-field realisations of the BMS$_3$ algebra and its extensions

TL;DR

This work constructs explicit free-field realizations of the $BMS_3$ algebra with nonzero central charges using a twisted β-γ system and explores extensions to supersymmetric and higher-spin ($W_3$) versions. Central charges are tunable by coupling to chiral matter, enabling arbitrary $c_1$ (via $c_1=c_0+26$ in the bosonic case) and a controllable $c_2$, while higher-spin and supersymmetric extensions are realized by adding fermionic ghosts and additional free fields. The authors obtain a free-field super-$BMS_3$ with $c_1=15$ and $c_2=12a$, and a $W_3$-BMS$_3$ realization with fixed $c_1=100$ alongside a tunable $c_2$, plus a partially realized SU(2)-BMS$_3$ via the Wakimoto construction. The results provide tractable models for flat-space holography and open avenues to study unitarity, bulk duals, and possible string-theoretic connections, with several directions left for generalization to higher $W_n$ algebras and BRST/topological implementations.

Abstract

We construct an explicit realisation of the BMS$_3$ algebra with nonzero central charges using holomorphic free fields. This can be extended by the addition of chiral matter to a realisation having arbitrary values for the two independent central charges. Via the introduction of additional free fields, we extend our construction to the minimally supersymmetric BMS$_3$ algebra and to the nonlinear higher-spin BMS$_3$-W$_3$ algebra. We also describe an extended system that realises both the SU(2) current algebra as well as BMS$_3$ via the Wakimoto representation, though in this case introducing a central extension also brings in new non-central operators.