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

TL;DR

The paper introduces a mechanism to realize AdS/CFT dual pairs with significantly smaller internal dimensions by employing 7-branes in F-theory to nearly cancel curvature energy, yielding a hierarchy where the AdS radius is parametrically larger than internal scales. It constructs explicit hierarchical AdS5/CFT4 examples via D3-branes at noncompact Calabi–Yau fourfold cones and extends the approach to AdS4/CFT3, detailing the near-horizon geometry, 7-brane moduli, and a criterion to avoid decompactification singularities. The authors derive the scaling of degrees of freedom and entropy, showing a parametric enhancement and providing an interpretation in terms of wound strings and Argyres-Douglas-like field theories. They also discuss the nature of the dual CFTs, potential non-toric generalizations, and prospects for cosmological holography, including possible de Sitter extensions via orientifolds and additional fluxes.

Abstract

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.