Maximal violation of Bell's inequalities for algebras of observables in tangent spacetime regions

We continue our study of Bell's inequalities and quantum field theory. It is shown in considerably broader generality than in our previous work that algebras of local observables corresponding to complementary wedge regions maximally violate Bell' inequalities in all normal states. Pairs of commuting von Neumann algebras that maximally violate Bell's inequalities in all normal states are characterized. Algebras of local observables corresponding to tangent double cones are shown to maximally violate Bell's inequalities in all normal states in dilatation-invariant theories, in free quantum field models, and in a class of interacting models. Further, it is proven that such algebras are not split in any theory with an ultraviolet scaling limit.