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

Chris Austin

Arxiv ID: 0704.1476•Last updated: 9/2/2022

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.

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