Gravitational Wilson Loop and Large Scale Curvature
arXiv:0706.2342 · doi:10.1103/PhysRevD.76.084008
Abstract
In a quantum theory of gravity the gravitational Wilson loop, defined as a suitable quantum average of a parallel transport operator around a large near-planar loop, provides important information about the large-scale curvature properties of the geometry. Here we shows that such properties can be systematically computed in the strong coupling limit of lattice regularized quantum gravity, by performing a local average over rotations, using an assumed near-uniform measure in group space. We then relate the resulting quantum averages to an expected semi-classical form valid for macroscopic observers, which leads to an identification of the gravitational correlation length appearing in the Wilson loop with an observed large-scale curvature. Our results suggest that strongly coupled gravity leads to a positively curved (De Sitter-like) quantum ground state, implying a positive effective cosmological constant at large distances.
22 pages, 6 figures
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- The phase and critical point of quantum Einstein-Cartan gravity
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- Scale-Dependent Newton's Constant G in the Conformal Newtonian Gauge
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- Geometric flux formula for the gravitational Wilson loop
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