Stabilization of submillimeter dimensions: The new guise of the hierarchy problem - art. no. 064020

A new framework for solving the hierarchy problem was recently proposed whi ch does not rely on low energy supersymmetry or technicolor. The fundamenta l Planck mass is at TeV and the observed weakness of gravity at long distan ces is due to the existence of new submillimeter spatial dimensions. In thi s picture the standard model fields are localized to a (3 + 1)-dimensional wall or ''3-brane.'' The hierarchy problem becomes isomorphic to the proble m of the largeness of the extra dimensions. This is in turn inextricably li nked to the cosmological constant problem, suggesting the possibility of a common solution. The radii of the extra dimensions must be prevented from b oth expanding to too great a size, and collapsing to the fundamental Planck length TeV-1. In this paper we propose a number of mechanisms addressing t his question. We argue that a positive bulk cosmological constant <(<Lambda >)over bar> can stabilize the internal manifold against expansion, and that the value of <(<Lambda>)over bar> is not unstable to radiative corrections provided that the supersymmetries of string theory are broken by dynamics on our 3-brane. We further argue that the extra dimensions can be stabilize d against collapse in a phenomenologically successful way by either of two methods: (1) large, topologically conserved quantum numbers associated with higher-form bulk U(1) gauge fields, such as the naturally occurring Ramond -Ramond gauge fields, or the winding number of bulk scalar fields; (2) the brane-lattice crystallization of a large number of 3-branes in the bulk. Th ese mechanisms are consistent with theoretical, laboratory, and cosmologica l considerations such as the absence of large time variations in Newton's c onstant during and after primordial nucleosynthesis, and millimeter-scale t ests of gravity.