Causally Disjoint Discs: Another $\mathbb{E}_n$-operad

Abstract

Motivated by (perturbative) quantum observables in Lorentzian signature we define a new operad: the operad of causally disjoint disks. In order to describe this operad we use the orthogonal categories of Benini, Schenkel, and Woike and the prefactorization functor of Benini, Carmona, Grant-Stuart, and Schenkel. Along the way we extend these constructions to the topological setting, i.e., (multi-)categories enriched over spaces.