Spectral dimension as a probe of the ultraviolet continuum regime of causal dynamical triangulations

TL;DR

This paper investigates the ultraviolet behavior of causal dynamical triangulations through spectral dimension flow, demonstrating that Hořava-Lifshitz gravity can replicate this flow in 2+1 dimensions, suggesting a deep theoretical connection.

Contribution

It establishes a framework linking spectral dimension flow in causal dynamical triangulations to continuum theories, specifically showing Hořava-Lifshitz gravity's ability to mimic this flow.

Findings

Hořava-Lifshitz gravity reproduces spectral dimension flow accurately

The framework connects discrete quantum gravity and continuum theories

Evidence of a significant link between CDT and Hořava-Lifshitz gravity

Abstract

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 behaviour of the latter in this regime. In particular, we show that, in 2+1 dimensions, Hovrava-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.