String-- and Brane--Localized Causal Fields in a Strongly Nonlocal Model

TL;DR

This paper investigates a weakly local yet maximally nonlocal quantum field model in higher dimensions, demonstrating the existence of string- and brane-localized operators that commute at spatial distances, and constructing local observables from nonlocal fields.

Contribution

It introduces a nonlocal quantum field model that still admits string- and brane-localized operators with commuting properties, and constructs local observables within a nonlocal framework.

Findings

Model is maximally nonlocal in a specific quantitative sense.

Existence of string- and brane-localized operators that commute at spatial distances.

Construction of a local subnet with a nontrivial scattering matrix in two dimensions.

Abstract

We study a weakly local, but nonlocal model in spacetime dimension $d \geq 2$ and prove that it is maximally nonlocal in a certain specific quantitative sense. Nevertheless, depending on the number of dimensions $d$, it has string--localized or brane--localized operators which commute at spatial distances. In two spacetime dimensions, the model even comprises a covariant and local subnet of operators localized in bounded subsets of Minkowski space which has a nontrivial scattering matrix. The model thus exemplifies the algebraic construction of local observables from algebras associated with nonlocal fields.