Causality in the brane world

TL;DR

This paper compares two candidate propagators in the Randall-Sundrum brane world model, demonstrating that only the Hankel function based propagator is causal and correctly implements junction conditions.

Contribution

It clarifies the causal structure and physical consistency of the propagators, showing the superiority of the Hankel function based approach over the normalized mode solution.

Findings

Hankel function based propagator is causal.

Normalized mode propagator supports outside the lightcone.

Only the Hankel propagator correctly implements junction conditions.

Abstract

For the Randall-Sundrum brane world where a positive tension Minkowski brane is embedded in AdS5, two candidate propagators have been suggested in the literature, one being based on the normalized mode solutions to the source-free volcano potential fluctuation equation, and the other being the Giddings, Katz and Randall outgoing Hankel function based one. We show that while both of these two propagators have the same pole plus cut singularity structure in the complex energy plane, they behave differently on their respective circles at infinity, as a consequence of which only the Hankel function based propagator proves to be causal, with the normalized mode based one being found to take support outside the AdS5 lightcone. In addition we show that unlike the Hankel function based propagator, the normalized mode based propagator does not correctly implement the junction conditions which hold in the presence of a perturbative source on the brane.