TeV-scale gravity in Horava-Witten theory on a compact complex hyperbolic threefold

Abstract

The field equations and boundary conditions of Horava-Witten theory, compactified on a smooth compact spin quotient of CH^3, where CH^3 denotes the hyperbolic cousin of CP^3, are studied in the presence of Casimir energy density terms. If the Casimir energy densities near one boundary result in a certain constant of integration taking a value greater than around 10^5 in units of the d = 11 gravitational length, a form of thick pipe geometry is found that realizes TeV-scale gravity by the ADD mechanism, with that boundary becoming the inner surface of the thick pipe, where we live. Three alternative ways in which the outer surface of the thick pipe might be stabilized consistent with the observed value of the effective d = 4 cosmological constant are considered. In the first alternative, the outer surface is stabilized in the classical region and the constant of integration is fixed at around 10^{13} in units of the d = 11 gravitational length for consistency with the observed cosmological constant. In the second alternative, the four observed dimensions have reduced in size down to the d = 11 gravitational length at the outer surface, and there are Casimir effects near the outer surface. In the third alternative, the outer surface is stabilized in the classical region by extra fluxes of the three-form gauge field, whose four-form field strength wraps three-cycles of the compact six-manifold times the radial dimension of the thick pipe. Some problems related to fitting the strong/electroweak Standard Model are considered.