Solving the Hierarchy Problem with Exponentially Large Dimensions

TL;DR

This paper proposes a mechanism where non-supersymmetric brane defects induce a logarithmic potential for extra dimensions, leading to exponentially large dimensions that address the hierarchy problem, with observable millimeter-range effects.

Contribution

It introduces a novel approach using logarithmic potentials from brane defects to naturally generate large extra dimensions solving the hierarchy problem.

Findings

Extra dimensions can be exponentially large due to logarithmic potentials.

The area modulus mediates millimeter-range Yukawa interactions.

The model remains consistent with high six-dimensional Planck scales.

Abstract

In theories with (sets of) two large extra dimensions and supersymmetry in the bulk, the presence of non-supersymmetric brane defects naturally induces a logarithmic potential for the volume of the transverse dimensions. Since the logarithm of the volume rather than the volume itself is the natural variable, parameters of O(10) in the potential can generate an exponentially large size for the extra dimensions. This provides a true solution to the hierarchy problem, on the same footing as technicolor or dynamical supersymmetry breaking. The area moduli have a Compton wavelength of about a millimeter and mediate Yukawa interactions with gravitational strength. We present a simple explicit example of this idea which generates two exponentially large dimensions. In this model, the area modulus mass is in the millimeter range even for six dimensional Planck scales as high as 100 TeV.