An Alternative to Compactification

TL;DR

The paper challenges the standard view that gravity requires compact extra dimensions by examining a non-factorizable geometry where a single 3-brane resides in AdS5. It shows that a bound graviton zero mode localizes four-dimensional gravity on the brane despite a continuous, gapless Kaluza-Klein spectrum, with corrections suppressed by the warp factor and curvature scale. The four-dimensional Planck scale arises from the 5D curvature, not the size of the extra dimension, and the regulator brane can be taken to infinity, yielding an infinite extra dimension. The work also discusses strong-coupling issues at large extra-dimensional coordinates but argues that low-energy brane processes remain effectively four-dimensional, offering a novel alternative to geometric compactification and opening avenues for connections to holography and conformal field theories.

Abstract

Conventional wisdom states that Newton's force law implies only four non-compact dimensions. We demonstrate that this is not necessarily true in the presence of a non-factorizable background geometry. The specific example we study is a single 3-brane embedded in five dimensions. We show that even without a gap in the Kaluza-Klein spectrum, four-dimensional Newtonian and general relativistic gravity is reproduced to more than adequate precision.