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 ĝλ, with BMS3 corresponding to the universal central extension of λ = −1. We construct the Becchi–Rouet–Stora–Tyutin (BRST) complex for ĝλ 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 realizations. We prove two theorems about the BRST cohomology of ĝλ. The first is the construction of a quasi-isomorphic embedding of the chiral sector of any Virasoro string as a ĝλ string. The second is the isomorphism (as Batalin–Vilkovisky algebras) of any ĝλ BRST cohomology and the chiral ring of a topologically twisted N = 2 superconformal field theory.