# Poisson vertex algebras in supersymmetric field theories

## TL;DR

This paper develops the mathematical framework of Poisson vertex algebras within the topological-holomorphic sectors of certain supersymmetric quantum field theories, linking algebraic structures to physical theories with extended supersymmetry.

## Contribution

It introduces Poisson vertex algebras in the context of supersymmetric field theories and explores their relation to local operators and algebraic limits in superconformal theories.

## Key findings

- Formulation of Poisson vertex algebras in supersymmetric sectors
- Examples illustrating the algebraic structures in specific theories
- Connection between Poisson vertex algebras and local operator algebras in superconformal theories

## Abstract

A large class of supersymmetric quantum field theories, including all theories with $\mathcal{N} = 2$ supersymmetry in three dimensions and theories with $\mathcal{N} = 2$ supersymmetry in four dimensions, possess topological-holomorphic sectors. We formulate Poisson vertex algebras in such topological-holomorphic sectors and discuss some examples. For a four-dimensional $\mathcal{N} = 2$ superconformal field theory, the associated Poisson vertex algebra is the classical limit of a vertex algebra generated by a subset of local operators of the theory.