Global causal propagator for the Klein-Gordon equation on a class of supersymmetric AdS backgrounds

TL;DR

This paper establishes the existence and explicit integral representation of a unique causal propagator for the Klein-Gordon equation on certain non-globally hyperbolic supergravity backgrounds, expanding understanding of wave propagation in complex geometries.

Contribution

It provides the first construction of a global causal propagator for Klein-Gordon on non-globally hyperbolic supersymmetric AdS backgrounds using spectral theory.

Findings

Existence of a unique admissible propagator.

Integral representation derived via spectral-theoretic methods.

Applicable to a class of Sasaki-Einstein manifolds.

Abstract

We analyze the Cauchy problem for the Klein-Gordon equation on the type IIB supergravity backgrounds $AdS^5 \times Y^{p,q}$, where $Y^{p,q}$ is any of the Sasaki-Einstein 5-manifolds recently discovered by Gaunlett, Martelli, Sparks and Waldram (Adv. Theor. Math. Phys. 8 (2004) 711--734). Although these spaces are not globally hyperbolic, we prove that there exists a unique admissible propagator and derive an integral representation thereof using spectral-theoretic techniques.