Logarithmic vertex algebras and non-local Poisson vertex algebras

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.