The BRST quantisation of chiral BMS-like field theories

The BMS₃ Lie algebra belongs to a one-parameter family of Lie algebras obtained by centrally extending abelian extensions of the Witt algebra by a tensor density representation. In this paper we call such Lie algebras g_, with BMS₃ corresponding to the universal central extension of = -1. We construct the BRST complex for g_ in two different ways: one in the language of semi-infinite cohomology and the other using the formalism of vertex operator algebras. We pay particular attention to the case of BMS₃ and discuss some natural field-theoretical realisations. We prove two theorems about the BRST cohomology of g_. The first is the construction of a quasi-isomorphic embedding of the chiral sector of any Virasoro string as a g_ string. The second is the isomorphism (as Batalin--Vilkovisky algebras) of any g_ BRST cohomology and the chiral ring of a topologically twisted N=2 superconformal field theory.