Scalar field Hadamard renormalisation in $AdS_{n}$

TL;DR

This paper develops an analytic Hadamard renormalisation method to compute the vacuum fluctuations and stress-energy tensor of a scalar field in anti-de Sitter spaces of dimensions 2 through 11.

Contribution

It provides explicit Hadamard renormalisation results for a massive scalar field with arbitrary curvature coupling in various $AdS_{n}$ spaces.

Findings

Explicit renormalised vacuum expectation values obtained for $n=2$ to $n=11$.

Method applicable to massive scalar fields with arbitrary curvature coupling.

Analytic expressions for stress-energy tensor components derived.

Abstract

We outline an analytic method for computing the renormalised vacuum expectation value of the quadratic fluctuations and stress-energy tensor associated with a quantised scalar field propagating on $AdS_{n}$. Explicit results have been obtained using Hadamard renormalisation in the case of a massive neutral scalar field with arbitrary coupling to the curvature, for $n=2$ to $n=11$ inclusive.