String- and brane-localized causal fields in a strongly nonlocal model

Abstract

We study a weakly local, but nonlocal model in spacetime dimension d >= 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 operators from algebras associated with nonlocal fields.