Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds

TL;DR

This paper constructs a sheaf of N=2 vertex algebras on Poisson manifolds, linking it to the chiral de Rham complex and classical supersymmetric models, revealing new geometric and algebraic structures.

Contribution

It introduces a sheaf of N=2 vertex algebras on Poisson manifolds and explores its relation to existing complexes and models, providing a manifest N=2 formalism.

Findings

Existence of a sheaf of N=2 vertex algebras on Poisson manifolds

Relation to the chiral de Rham complex

Connection to classical supersymmetric sigma models

Abstract

We construct a sheaf of N=2 vertex algebras naturally associated to any Poisson manifold. The relation of this sheaf to the chiral de Rham complex is discussed. We reprove the result about the existence of two commuting N = 2 superconformal structures on the space of sections of the chiral de Rham complex of a Calabi-Yau manifold, but now calculated in a manifest N=2 formalism. We discuss how the semi-classical limit of this sheaf of N=2 vertex algebras is related to the classical supersymmetric non-linear sigma model.