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+Dz. 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.
CITATION STYLE
Hořava, P. (2009). Spectral dimension of the universe in quantum gravity at a lifshitz point. Physical Review Letters, 102(16). https://doi.org/10.1103/PhysRevLett.102.161301
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