CDT meets Horava-Lifshitz gravity

TL;DR

Ambjørn et al. investigate whether causal dynamical triangulations (CDT) exhibit a Lifshitz-type phase structure akin to Hořava-Lifshitz gravity. By mapping CDT's three phases A, B, and C to Lifshitz-like regimes, they illustrate how CDT could serve as a nonperturbative lattice framework for both anisotropic HL dynamics and isotropic renormalization-group scenarios, potentially identifying UV fixed points along phase boundaries or at endpoints. The work emphasizes the role of a global time foliation, conformal-mode dynamics, and time-space anisotropy in bridging CDT with HL gravity and RG-based asymptotic safety, while acknowledging finite-size limitations. Overall, the paper proposes CDT as a universal lattice template for understanding nonperturbative higher-dimensional quantum gravity and highlights key transitions and endpoints that warrant further numerical exploration.

Abstract

The theory of causal dynamical triangulations (CDT) attempts to define a nonperturbative theory of quantum gravity as a sum over space-time geometries. One of the ingredients of the CDT framework is a global time foliation, which also plays a central role in the quantum gravity theory recently formulated by Hořava. We show that the phase diagram of CDT bears a striking resemblance with the generic Lifshitz phase diagram appealed to by Hořava. We argue that CDT might provide a unifying nonperturbative framework for anisotropic as well as isotropic theories of quantum gravity.

Figures (3)

• Figure 1: The phase diagram of four-dimensional quantum gravity, defined in terms of causal dynamical triangulations, parametrized by the inverse bare gravitational coupling $\kappa_0$ and the asymmetry $\Delta$.
• Figure 2: Evidence for a first-order signal at the A-C phase transition.
• Figure 3: Evidence for a first-order signal at the B-C phase transition -- or is it?