A concrete construction of a topological operator in factorization algebras

TL;DR

This paper presents a concrete method to construct a topological operator within the framework of factorization algebras, specifically applied to a one-dimensional scalar theory, enhancing the mathematical tools for quantum field theories.

Contribution

It introduces a new explicit construction of a topological operator in factorization algebras, focusing on shift symmetry and $ heta$-vacuum in scalar theories.

Findings

Constructed a topological operator explicitly within factorization algebras.

Analyzed the shift symmetry in a 1D massless scalar theory.

Discussed $ heta$-vacuum and $ ext{Z}$-gauging effects.

Abstract

Factorization algebras play a central role in the formulation of quantum field theories given by Kevin Costello and his collaborators. In this paper, we propose a concrete construction of a topological operator in their formulation. We focus on a shift symmetry of a one-dimensional massless scalar theory. And we give some discussions of $\mathbb{Z}$-gauging of it, i.e., compact scalar theory and its $\theta$-vacuum.