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

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.

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Published 1 January 2010