The BRST quantisation of chiral BMS-like field theories

Abstract

The BMS${}_3$ 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 ${\hat{\mathfrak{g}}}_{\lambda }$, with BMS${}_3$ corresponding to the universal central extension of $\lambda =-1$. We construct the BRST complex for ${\hat{\mathfrak{g}}}_{\lambda }$ 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 BMS${}_3$ and discuss some natural field-theoretical realisations. We prove two theorems about the BRST cohomology of ${\hat{\mathfrak{g}}}_{\lambda }$. The first is the construction of a quasi-isomorphic embedding of the chiral sector of any Virasoro string as a ${\hat{\mathfrak{g}}}_{\lambda }$ string. The second is the isomorphism (as Batalin-Vilkovisky algebras) of any ${\hat{\mathfrak{g}}}_{\lambda }$ BRST cohomology and the chiral ring of a topologically twisted $N=2$ superconformal field theory.

arXiv commentv2: 28 pages. Fixed typos and added some references

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• AdS${}_3$ Carroll gravity: asymptotic symmetries and C-thermal configurations
• String theory in twistor space and minimal tension holography