A concrete construction of a topological operator in factorization algebras

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.