2,002 research outputs found
The Generalized Ricci Flow for 3D Manifolds with One Killing Vector
We consider 3D flow equations inspired by the renormalization group (RG)
equations of string theory with a three dimensional target space. By modifying
the flow equations to include a U(1) gauge field, and adding carefully chosen
De Turck terms, we are able to extend recent 2D results of Bakas to the case of
a 3D Riemannian metric with one Killing vector. In particular, we show that the
RG flow with De Turck terms can be reduced to two equations: the continual Toda
flow solved by Bakas, plus its linearizaton. We find exact solutions which flow
to homogeneous but not always isotropic geometries
Corrections to Gravity due to a Sol Manifold Extra Dimensional Space
The corrections to the gravitational potential due to a Sol extra dimensional
compact manifold, denoted as , are studied. The total spacetime is of
the form . The range of the Sol corrections is investigated
and compared to the range of the corrections.Comment: 13 pages, 10 figures, published versio
Circles in the Sky: Finding Topology with the Microwave Background Radiation
If the universe is finite and smaller than the distance to the surface of
last scatter, then the signature of the topology of the universe is writ large
on the microwave background sky. We show that the microwave background will be
identified at the intersections of the surface of last scattering as seen by
different ``copies'' of the observer. Since the surface of last scattering is a
two-sphere, these intersections will be circles, regardless of the background
geometry or topology. We therefore propose a statistic that is sensitive to all
small, locally homogeneous topologies. Here, small means that the distance to
the surface of last scatter is smaller than the ``topology scale'' of the
universe.Comment: 14 pages, 10 figures, IOP format. This paper is a direct descendant
of gr-qc/9602039. To appear in a special proceedings issue of Class. Quant.
Grav. covering the Cleveland Topology & Cosmology Worksho
Reconstructing the global topology of the universe from the cosmic microwave background
If the universe is multiply-connected and sufficiently small, then the last
scattering surface wraps around the universe and intersects itself. Each circle
of intersection appears as two distinct circles on the microwave sky. The
present article shows how to use the matched circles to explicitly reconstruct
the global topology of space.Comment: 6 pages, 2 figures, IOP format. To be published in the proceedings of
the Cleveland Cosmology and Topology Workshop 17-19 Oct 1997. Submitted to
Class. Quant. Gra
Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
We construct an exactly solvable Hamiltonian acting on a 3-dimensional
lattice of spin- systems that exhibits topological quantum order.
The ground state is a string-net and a membrane-net condensate. Excitations
appear in the form of quasiparticles and fluxes, as the boundaries of strings
and membranes, respectively. The degeneracy of the ground state depends upon
the homology of the 3-manifold. We generalize the system to , were
different topological phases may occur. The whole construction is based on
certain special complexes that we call colexes.Comment: Revtex4 file, color figures, minor correction
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