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APS » Journals » Phys. Rev. Lett. » Volume 102 » Issue 16
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Phys. Rev. Lett. 102, 161301 (2009) [4 pages]

Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point

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Petr Hořava
Berkeley Center for Theoretical Physics, University of California, Berkeley, California 94720-7300, USA and Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720-8162, USA

Received 27 February 2009; published 20 April 2009

See accompanying Physics Synopsis

We extend the definition of “spectral dimension” ds (usually defined for fractal and lattice geometries) to theories in spacetimes with anisotropic scaling. We show that in gravity with dynamical critical exponent z in D+1 dimensions, the spectral dimension of spacetime is ds=1+D/z. In the case of gravity in 3+1 dimensions with z=3 in the UV which flows to z=1 in the IR, the spectral dimension changes from ds=4 at large scales to ds=2 at short distances. Remarkably, this is the behavior found numerically by Ambjørn et al. in their causal dynamical triangulations approach to quantum gravity.

© 2009 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.102.161301
DOI:
10.1103/PhysRevLett.102.161301
PACS:
04.60.Nc
 
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