Stable quantum systems in anti-de Sitter space: Causality, independence and spectral properties

TL;DR

This paper explores the stability, causality, and independence properties of quantum states in anti-de Sitter space, revealing universal temperature, symmetry, and locality features that are model-independent and applicable to various theories.

Contribution

It demonstrates that passive states in AdS induce a geodesic causal structure and strong independence conditions, enabling the derivation of local covariant nets in two-dimensional AdS.

Findings

Passive states exhibit a universal Unruh temperature.

Observables in complementary regions commute in passive states.

In 2D AdS, local covariant nets can be constructed.

Abstract

If a state is passive for uniformly accelerated observers in n-dimensional anti-de Sitter space-time (i.e. cannot be used by them to operate a perpetuum mobile), they will (a) register a universal value of the Unruh temperature, (b) discover a PCT symmetry, and (c) find that observables in complementary wedge-shaped regions necessarily commute with each other in this state. The stability properties of such a passive state induce a "geodesic causal structure" on AdS and concommitant locality relations. It is shown that observables in these complementary wedge-shaped regions fulfill strong additional independence conditions. In two-dimensional AdS these even suffice to enable the derivation of a nontrivial, local, covariant net indexed by bounded spacetime regions. All these results are model-independent and hold in any theory which is compatible with a weak notion of space-time localization. Examples are provided of models satisfying the hypotheses of these theorems.