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

Abstract

We analyze the Cauchy problem for the Klein–Gordon equation on the type IIB supergravity backgrounds $\mathrm{AdS}^5 \times Y^{p,q}$, where $Y^{p,q}$ is any of the Sasaki–Einstein 5-manifolds introduced by Gaunlett et al. (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.