2009/02/28 by Petr Horava
Physics and Astronomy · #hep-th #gr-qc #hep-lat #hep-ph
paper · pdf · doi:10.1103/physrevlett.102.161301
published as Phys.Rev.Lett.102:161301,2009 · 11 pages, 1 figure; v2: typos corrected
arxiv created 2009/03/03 · arxiv updated 2009/12/01
We extend the definition of "spectral dimension" (usually defined for fractal and lattice geometries) to theories on smooth spacetimes with anisotropic scaling. We show that in quantum gravity dominated by a Lifshitz point with dynamical critical exponent z in D+1 spacetime dimensions, the spectral dimension of spacetime is equal to ds=1+D/z. In the case of gravity in 3+1 dimensions presented in arXiv:0901.3775, which is dominated by z=3 in the UV and flows to z=1 in the IR, the spectral dimension of spacetime flows from ds=4 at large scales, to ds=2 at short distances. Remarkably, this is the qualitative behavior of ds found numerically by Ambjorn, Jurkiewicz and Loll in their causal dynamical triangulations approach to quantum gravity.