Quantum Scalar Fields on Anti-de Sitter Spacetime

TL;DR

This paper computes quantum scalar field effects on hyperbolic and anti-de Sitter spaces using zeta-function regularization, providing exact results for the effective action, fluctuations, and stress tensor.

Contribution

It applies and tests a direct zeta-function technique to compute quantum effects on hyperbolic spaces, relevant for anti-de Sitter spacetime, with exact analytical results.

Findings

Exact one-loop effective action computed.

Vacuum fluctuations and stress tensor evaluated.

Method validated for continuous spectrum scenarios.

Abstract

We investigate the propagation of arbitrarily coupled scalar fields on the $N$-dimensional hyperbolic space ${\mathbb H}^N$. Using the $\zeta$-function regularization we compute exactly the one loop effective action. The vacuum expectation value of quadratic field fluctuations and the one loop renormalized stress tensor are then computed using the recently proposed direct $\zeta$-function technique. Our computation tests the validity of this approach in presence of a continuous spectrum. Our results apply as well to the $N$-dimensional anti-de Sitter spacetime, whose appropriate euclidean section is the hyperbolic space ${\mathbb H}^N$.