Raviolo vertex algebras

TL;DR

This paper introduces raviolo vertex algebras, a new algebraic framework for modeling local operators in 3D quantum field theories that are partially holomorphic and topological, inspired by geometric structures called raviolos.

Contribution

It develops the foundational theory of raviolo vertex algebras, establishing structure theorems and providing illustrative examples that parallel classical vertex algebra theory.

Findings

Raviolo vertex algebras model 3D QFT local operators.

Structure theorems analogous to vertex algebras are proven.

Examples exhibit similarities to classical vertex algebras.

Abstract

We develop an algebraic structure modeling local operators in a three-dimensional quantum field theory which is partially holomorphic and partially topological. The geometric space organizing our algebraic structure is called the raviolo (or bubble) and replaces the punctured disk underlying vertex algebras; we refer to this structure as a raviolo vertex algebra. The raviolo has appeared in many contexts related to three-dimensional supersymmetric gauge theory, especially in work on the affine Grassmannian. We prove a number of structure theorems for raviolo vertex algebras and provide simple examples that share many similarities with their vertex algebra counterparts.