Hadamard renormalized scalar field theory on anti-de Sitter space-time

TL;DR

This paper computes the vacuum expectation values of scalar field fluctuations and stress-energy tensor in anti-de Sitter space-time using Hadamard renormalization, providing explicit results for dimensions 2 through 11.

Contribution

It applies Hadamard renormalization to derive explicit vacuum expectation values for scalar fields in various dimensions of anti-de Sitter space.

Findings

Explicit vacuum expectation values for scalar fields in dimensions 2 to 11.

Demonstrates the use of Hadamard renormalization in curved space-time.

Provides analytical results for stress-energy tensor components.

Abstract

We consider a real massive free quantum scalar field with arbitrary curvature coupling on $n$-dimensional anti-de Sitter space-time. We use Hadamard renormalization to find the vacuum expectation values of the quadratic field fluctuations and the stress-energy tensor, presenting explicit results for $n=2$ to $n=11$ inclusive.