Stabilization of Sub-Millimeter Dimensions: The New Guise of the
Hierarchy Problem
ArXiv hep-th/9809124 (1998)
Authors:
Nima Arkani-Hamed, Savas Dimopoulos, John March-Russell
Abstract:
A new framework for solving the hierarchy problem was recently proposed which
does not rely on low energy supersymmetry or technicolor. The fundamental
Planck mass is at a $\tev$ and the observed weakness of gravity at long
distances is due the existence of new sub-millimeter spatial dimensions. In
this picture the standard model fields are localized to a $(3+1)$-dimensional
wall or ``3-brane''. The hierarchy problem becomes isomorphic to the problem of
the largeness of the extra dimensions. This is in turn inextricably linked to
the cosmological constant problem, suggesting the possibility of a common
solution. The radii of the extra dimensions must be prevented from both
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 this
question. We argue that a positive bulk cosmological constant $\bar\Lambda$ can
stabilize the internal manifold against expansion, and that the value of
$\bar\Lambda$ 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 stabilized 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. These mechanisms are consistent with
theoretical, laboratory, and cosmological considerations such as the absence of
large time variations in Newton's constant during and after primordial
nucleosynthesis, and millimeter-scale tests of gravity.
