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

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 Ambj{}rn et al. in their causal dynamical triangulations approach to quantum gravity.