Towards a General Theory of Quantized Fields on the Anti-de Sitter Space-Time

TL;DR

This paper develops a comprehensive framework for quantum field theory on anti-de Sitter space-time, establishing key properties of n-point functions, Wick rotation, and the AdS-Unruh effect for specific accelerated observers.

Contribution

It introduces a general, positivity-based framework for QFT on AdS, characterizes two-point functions, and demonstrates the AdS-Unruh effect for certain accelerated trajectories.

Findings

n-point functions are analytic in complex AdS domains

Wick rotation to Euclidean space is possible and consistent

AdS-Unruh effect exists for specific accelerated observers crossing the boundary

Abstract

We propose a general framework for studying quantum field theory on the anti-de-Sitter space-time, based on the assumption of positivity of the spectrum of the possible energy operators. In this framework we show that the n-point functions are analytic in suitable domains of the complex AdS manifold, that it is possible to Wick rotate to the Euclidean manifold and come back, and that it is meaningful to restrict AdS quantum fields to Poincare' branes. We give also a complete characterization of two-point functions which are the simplest example of our theory. Finally we prove the existence of the AdS-Unruh effect for uniformly accelerated observers on trajectories crossing the boundary of AdS at infinity, while that effect does not exist for all the other uniformly accelerated trajectories.