is a ground state; uniformly accelerated observers in AdS will register a universal value of the Unruh temperature; they will discover a PCT symmetry; and they will find that observables localized in complementary wedge–shaped regions must commute in the vacuum state. Not only do such observables commute in this sense, but the corresponding algebras manifest strong properties of statistical independence, the nature of which will be studied in detail. We shall also see that these assumptions imply that quantum theories on AdS obey a geodesic causal structure.

Related results appeared in [@AdS], and we revisit some of those arguments here in more detail than in that announcement. But our research in the intervening time has led not only to further results and a weakening of the assumptions, but also to a shift in our point of view, which now places emphasis on the locality and independence properties which can be derived from our assumptions. We establish independence properties going far beyond those announced in [@AdS], and we prove an additional locality property of such theories on proper which was not observed in [@AdS]. Moreover, we show that in two dimensions these suffice to construct a nontrivial, local, covariant net indexed 