Chiral algebras with abelian conformal part

Abstract

We study a categorical approach to the concept of varieties of chiral algebras. We prove that the class of chiral algebras in the variety defined by a binary quadratic operad Var, whose conformal structure is abelian, coincides with the class of differential algebras in the variety defined by the Manin black product of the operads Var and Com, where Com is the operad of associative commutative algebras.