The second law of thermodynamics, TCP, and Einstein causality in anti-de Sitter space-time

TL;DR

This paper explores fundamental thermodynamic and causality principles in anti-de Sitter space-time, revealing universal temperature, symmetry, and locality properties for accelerated observers, with implications for quantum field theory and gravity.

Contribution

It demonstrates that vacuum states in anti-de Sitter space-time exhibit universal thermodynamic and causality features, independent of specific models, under weak localization assumptions.

Findings

Observers detect a universal Hawking-Unruh temperature.

A TCP symmetry is observed in the vacuum state.

Local observables in complementary regions are commensurable.

Abstract

If the vacuum is passive for uniformly accelerated observers in 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 Hawking-Unruh temperature, (b) discover a TCP symmetry, and (c) find that observables in complementary wedge-shaped regions are commensurable (local) in the vacuum state. These results are model independent and hold in any theory which is compatible with some weak notion of space-time localization.