Deformation quantization of vertex Poisson algebras

TL;DR

This paper develops a theoretical framework using dg Lie algebras to study the deformation quantization of vertex Poisson algebras into vertex algebras, connecting operadic and chiral algebra theories.

Contribution

It introduces a new approach employing dg Lie algebras and operadic methods to analyze deformations of vertex Poisson algebras, advancing the mathematical understanding of quantization in this context.

Findings

Formulation of dg Lie algebras controlling deformations

Connection between vertex Poisson and vertex algebras

Framework for deformation quantization

Abstract

We introduce dg Lie algebras controlling the deformations of vertex algebras and vertex Poisson algebras, utilizing the notion of operadic dg Lie algebra and the theory of chiral algebra. In terms of those dg Lie algebras, we formulate the deformation quantization problem of vertex Poisson algebras to vertex algebras.