Dual Purpose Landscaping Tools: Small Extra Dimensions in AdS/CFT

We propose a class of AdS/CFT dual pairs which have small internal dimensionson the gravity side. Starting from known Freund-Rubin AdS/CFT dual pairs, weuse 7-branes to nearly cancel the curvature energy of the internal dimensionswhile maintaining their stabilization. This leads to a new corner of thelandscape - a class of AdS solutions with a hierarchically large AdS radius -with a dual field theory given (implicitly) by the infrared limit of a concretebrane construction involving D3-branes, 7-branes, and curvature. We firstconstruct a class of hierarchical AdS5/CFT4 dual pairs with a simple formulafor the number of degrees of freedom which we interpret in the dual QFT. Wethen generalize these to AdS4/CFT3 duals, and suggest extensions of the methodto obtain de Sitter solutions.