Gauge theories on hyperbolic spaces and dual wormhole instabilities

We study supergravity duals of strongly coupled four dimensional gauge theories formulated on compact quotients of hyperbolic spaces. The resulting background geometries are represented by Euclidean wormholes, which complicates establishing the precise gauge theory/string theory correspondence dictionary. These backgrounds suffer from the non-perturbative instabilities arising from the D3 - anti-D3 pair production in the background four-form potential. We discuss conditions for suppressing this Schwinger-like instability. We find that Euclidean wormholes arising in this construction develop a naked singularity, before they can be stabilized.