160,670 research outputs found
The SO(32) Heterotic and Type IIB Membranes
A two dimensional anomaly cancellation argument is used to construct the
SO(32) heterotic and type IIB membranes. By imposing different boundary
conditions at the two boundaries of a membrane, we shift all of the two
dimensional anomaly to one of the boundaries. The topology of these membranes
is that of a 2-dimensional cone propagating in the 11-dimensional target space.
Dimensional reduction of these membranes yields the SO(32) heterotic and type
IIB strings.Comment: 12 pages, Late
The visual boundary of Z^2
We introduce ideas from geometric group theory related to boundaries of
groups. This is a mostly expository paper. We consider the visual boundary of a
free abelian group, and show that it is an uncountable set with the trivial
topology
Four Dimensional Quantum Topology Changes of Spacetimes
We investigate topology changing processes in the WKB approximation of four
dimensional quantum cosmology with a negative cosmological constant. As
Riemannian manifolds which describe quantum tunnelings of spacetime we consider
constant negative curvature solutions of the Einstein equation i.e. hyperbolic
geometries. Using four dimensional polytopes, we can explicitly construct
hyperbolic manifolds with topologically non-trivial boundaries which describe
topology changes. These instanton-like solutions are constructed out of
8-cell's, 16-cell's or 24-cell's and have several points at infinity called
cusps. The hyperbolic manifolds are non-compact because of the cusps but have
finite volumes. Then we evaluate topology change amplitudes in the WKB
approximation in terms of the volumes of these manifolds. We find that the more
complicated are the topology changes, the more likely are suppressed.Comment: 26 pages, revtex, 13 figures. The calculation of volume and
grammatical errors are correcte
Future Foam
We study pocket universes which have zero cosmological constant and
non-trivial boundary topology. These arise from bubble collisions in eternal
inflation. Using a simplified dust model of collisions we find that boundaries
of any genus can occur. Using a radiation shell model we perform analytic
studies in the thin wall limit to show the existence of geometries with a
single toroidal boundary. We give plausibility arguments that higher genus
boundaries can also occur. In geometries with one boundary of any genus a
timelike observer can see the entire boundary. Geometries with multiple
disconnected boundaries can also occur. In the spherical case with two
boundaries the boundaries are separated by a horizon. Our results suggest that
the holographic dual description for eternal inflation, proposed by Freivogel,
Sekino, Susskind and Yeh, should include summation over the genus of the base
space of the dual conformal field theory. We point out peculiarities of this
genus expansion compared to the string perturbation series.Comment: 23 pages, 6 figure
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