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Logarithmic Vertex Algebras and Non-local Poisson Vertex Algebras
OAI: oai:purehost.bath.ac.uk:openaire_cris_publications/ffe34e65-3645-4709-8ea0-2c93ff8eef2b • DOI: https://doi.org/10.1007/s00220-023-04839-x
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.