## Abstract

Logarithmic vertex algebras were introduced in our previous paper, motivated by logarithmic conformal field theory (Bakalov and Villarreal in Logarithmic vertex algebras, 2022). Non-local Poisson vertex algebras were introduced by De Sole and Kac, motivated by the theory of integrable systems (De Sole and Kac in Jpn J Math 8:233–347, 2013). We prove that the associated graded vector space of any filtered logarithmic vertex algebra has an induced structure of a non-local Poisson vertex algebra. We use this relation to obtain new examples of both logarithmic vertex algebras and non-local Poisson vertex algebras.

Original language | English |
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Pages (from-to) | 185-226 |

Number of pages | 42 |

Journal | Communications in Mathematical Physics |

Volume | 404 |

Issue number | 1 |

Early online date | 5 Sept 2023 |

DOIs | |

Publication status | Published - 5 Sept 2023 |

### Bibliographical note

Funding Information:The first author was supported in part by a Simons Foundation grant 584741. The second author was supported in part by UK Research and Innovation grant MR/S032657/1.

### Funding

The first author was supported in part by a Simons Foundation grant 584741. The second author was supported in part by UK Research and Innovation grant MR/S032657/1. The second author thanks Marco Aldi for stimulating discussions on a related subject. He is grateful to Tomoyuki Arakawa and the organizers of the conference Vertex Algebras and Representation Theory at CIRM in June 2022, where some of the results of this work were announced. Both authors are grateful to Nikolay M. Nikolov for interesting discussions, and to the Institute for Nuclear Research and Nuclear Energy of the Bulgarian Academy of Sciences for the hospitality during June 2022.

Funders | Funder number |
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Tomoyuki Arakawa | |

Simons Foundation | 584741 |

California Institute for Regenerative Medicine | |

UK Research and Innovation | MR/S032657/1 |

Bulgarian Academy of Sciences |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics