Dual purpose landscaping tools: Small extra dimensions in AdS/CFT

We propose a class of AdS/CFT dual pairs which have small internal dimensions on the gravity side. Starting from known Freund–Rubin AdS/CFT dual pairs, we use 7-branes to nearly cancel the curvature energy of the internal dimensions while maintaining their stabilization. This leads to a new corner of the landscape — a class of AdS solutions with a hierarchically large AdS radius — with a dual field theory given (implicitly) by the infrared limit of a concrete brane construction involving D3-branes, 7-branes, and curvature. We first construct a class of hierarchical AdS5/CFT4 dual pairs with a simple formula for the number of degrees of freedom which we interpret in the dual QFT. We then generalize these to AdS4/CFT3 duals, and suggest extensions of the method to obtain de Sitter solutions.