Spectral Dimension as a Probe of the Ultraviolet Continuum Regime of Causal Dynamical Triangulations

We explore the ultraviolet continuum regime of causal dynamical triangulations, as probed by the flow of the spectral dimension. We set up a framework in which one can find continuum theories that can in principle fully reproduce the behavior of the latter in this regime. In particular, we show that, in 2 + 1 dimensions, Horava-Lifshitz gravity can mimic the flow of the spectral dimension in causal dynamical triangulations to high accuracy and over a wide range of scales. This seems to provide evidence for an important connection between the two theories.