Notes on Factorization Algebras and TQFTs

TL;DR

This paper introduces the role of factorization algebras in topological quantum field theories, exploring their connections with $ ext{E}_n$-algebras, vertex algebras, and the functorial approach to field theories.

Contribution

It provides an accessible overview of how factorization algebras relate to various algebraic structures in field theory, emphasizing their conceptual and practical significance.

Findings

Clarifies the relationship between factorization algebras and $ ext{E}_n$-algebras

Explores connections between factorization algebras and vertex algebras

Highlights the functorial perspective on topological quantum field theories

Abstract

These are notes from talks given at a spring school on topological quantum field theory in Nova Scotia during May of 2023. The aim is to introduce the reader to the role of factorization algebras and related concepts in field theory. In particular, we discuss the relationship between factorization algebras, $\mathbb{E}_n$-algebras, vertex algebras, and the functorial perspective on field theories.