Free-field realisations of the BMS3 algebra and its extensions

Abstract

We construct an explicit realisation of the BMS3 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 BMS3 algebra and to the nonlinear higher-spin BMS3-W3 algebra. We also describe an extended system that realises both the SU(2) current algebra as well as BMS3 via the Wakimoto representation, though in this case introducing a central extension also brings in new non-central operators.