Logarithmic vertex algebras and non-local Poisson vertex algebras

TL;DR

This paper establishes a connection between logarithmic vertex algebras and non-local Poisson vertex algebras, providing new examples and insights into their structures within mathematical physics.

Contribution

It proves that the associated graded space of any filtered logarithmic vertex algebra naturally inherits a non-local Poisson vertex algebra structure.

Findings

Established a structural link between logarithmic vertex algebras and non-local Poisson vertex algebras

Constructed new examples of both algebraic structures

Enhanced understanding of algebraic frameworks in logarithmic conformal field theory

Abstract

Logarithmic vertex algebras were introduced in our previous paper, motivated by logarithmic conformal field theory. Non-local Poisson vertex algebras were introduced by De Sole and Kac, motivated by the theory of integrable systems. 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. Dedicated to Victor G. Kac on his 80th birthday.