The BRST quantisation of chiral BMS-like field theories
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arXiv
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| Format: | Preprint |
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2024
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| author | Figueroa-O'Farrill, José Vishwa, Girish S |
| author_facet | Figueroa-O'Farrill, José Vishwa, Girish S |
| contents | 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 $\hat{\mathfrak{g}}_λ$, with BMS$_3$ corresponding to the universal central extension of $λ= -1$. We construct the BRST complex for $\hat{\mathfrak{g}}_λ$ 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 $\hat{\mathfrak{g}}_λ$. The first is the construction of a quasi-isomorphic embedding of the chiral sector of any Virasoro string as a $\hat{\mathfrak{g}}_λ$ string. The second is the isomorphism (as Batalin-Vilkovisky algebras) of any $\hat{\mathfrak{g}}_λ$ BRST cohomology and the chiral ring of a topologically twisted $N{=}2$ superconformal field theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_12778 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The BRST quantisation of chiral BMS-like field theories Figueroa-O'Farrill, José Vishwa, Girish S High Energy Physics - Theory Mathematical Physics 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 $\hat{\mathfrak{g}}_λ$, with BMS$_3$ corresponding to the universal central extension of $λ= -1$. We construct the BRST complex for $\hat{\mathfrak{g}}_λ$ 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 $\hat{\mathfrak{g}}_λ$. The first is the construction of a quasi-isomorphic embedding of the chiral sector of any Virasoro string as a $\hat{\mathfrak{g}}_λ$ string. The second is the isomorphism (as Batalin-Vilkovisky algebras) of any $\hat{\mathfrak{g}}_λ$ BRST cohomology and the chiral ring of a topologically twisted $N{=}2$ superconformal field theory. |
| title | The BRST quantisation of chiral BMS-like field theories |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2407.12778 |