Solving the Hierarchy Problem with Noncompact Extra Dimensions

TL;DR

The paper proposes a noncompact, exponentially large transverse dimension scenario to address the hierarchy problem, realized by the spacetime around a global cosmic string in $d+2$ dimensions. By solving Einstein's equations and imposing unitary boundary conditions at a mild naked singularity, it shows a finite transverse radius and an exponentially enhanced 4D Planck scale relative to the bulk scale, without fine-tuning. The analysis yields a massless 4D graviton bound to the brane and a discrete, non-tachyonic Kaluza-Klein spectrum with small mass gaps, making the model phenomenologically viable and closely related to large extra dimensions. The framework also discusses stability, potential generalizations to other codimensions, and speculative links between bulk topology and brane family structure.

Abstract

We show that gravitational effects of global cosmic 3-branes can be responsible for compactification from six to four space-time dimensions, naturally producing the observed hierarchy between electroweak and gravitational forces. The finite radius of the transverse dimensions follows from Einstein's equation, and is exponentially large compared with the scales associated with the 3-brane. The space-time ends on a mild naked singularity at the boundary of the transverse dimensions; nevertheless unitary boundary conditions render the singularity harmless.