Quantum Gravity from Causal Dynamical Triangulations: A Review (1905.08669v1)

Abstract: This topical review gives a comprehensive overview and assessment of recent results in Causal Dynamical Triangulations (CDT), a modern formulation of lattice gravity, whose aim is to obtain a theory of quantum gravity nonperturbatively from a scaling limit of the lattice-regularized theory. In this manifestly diffeomorphism-invariant approach one has direct, computational access to a Planckian spacetime regime, which is explored with the help of invariant quantum observables. During the last few years, there have been numerous new and important developments and insights concerning the theory's phase structure, the roles of time, causality, diffeomorphisms and global topology, the application of renormalization group methods and new observables. We will focus on these new results, primarily in four spacetime dimensions, and discuss some of their geometric and physical implications.

• The paper introduces CDT as a nonperturbative approach that reveals a semiclassical de Sitter universe emerging in quantum gravity.
• It employs Monte Carlo simulations to map the phase structure and identify second-order transitions crucial for achieving a continuum limit.
• The study highlights numerical methods and invariant observables, offering practical insights for testing theoretical models of quantum gravity.

Quantum Gravity from Causal Dynamical Triangulations: A Review

Overview

The paper "Quantum Gravity from Causal Dynamical Triangulations: A Review" by R. Loll provides a comprehensive examination of the developments in Causal Dynamical Triangulations (CDT) as a framework for quantum gravity. This approach attempts to derive a nonperturbative theory of quantum gravity by considering a scaling limit of a lattice-regularized theory, maintaining a manifestly diffeomorphism-invariant formulation. CDT leverages the concept of Lorentzian geometries, diverging from traditional Euclidean approaches, and seeks direct computational access to the Planckian regime of spacetime through invariant quantum observables.

Phase Structure and Observations

Significant strides have been made in understanding CDT’s phase structure. Notably, the work achieved remarkable progress in revealing the multi-phase nature of the theory. Particularly in four dimensions, an emergent "de Sitter" universe with semiclassical characteristics has been identified within one of the theory's phases. Further investigations revealed a dynamical dimensional reduction at Planckian scales, sparking interest in measuring the spectral dimension under quantum gravitational models.

Additionally, the work reported strong evidence supporting second-order phase transitions, crucial for the continuum limit of the lattice theory, showcasing transitions not evident in other four-dimensional quantum gravity models. The phase structure of CDT continues to provide a fertile ground for exploring the implications of various geometrical and physical properties, with new observables such as gravitational Wilson loops and quantum Ricci curvature being introduced.

Computational Framework and Numerical Techniques

The numerical methods applied within CDT have leveraged Monte Carlo simulations effectively, becoming a key strength of the formulation. These methods allow for probing complex regimes of quantum gravity that remain inaccessible through purely analytical approaches. Noteworthy numerical simulations have explored the possibility of higher-order transitions, the emergence of classical geometries, and the application of renormalization group concepts.

CDT maintains its Lorentzian characteristics through a rigorous Wick rotation enabling the evaluation of path integrals, demonstrated successfully in two dimensions, illustrating potential deviations from Euclidean formulations. The computational lab established via CDT enables empirical tests of theoretical conjectures, an aspect critical for advancing the frontier of quantum gravity.

Theoretical and Practical Implications

The implications of CDT in quantum gravity research are significant. The framework not only underscores the existence of a semiclassical limit, aligning with classical theories, but also allows for the examination of new quantum phenomena, such as evidence for a scale-dependent change in spacetime dimensionality. These insights contribute to a deeper understanding of the nonperturbative structure of spacetime and hold potential for informing the development of a consistent theory of quantum gravity.

On a theoretical level, CDT elucidates the role of causality and topology in the nonperturbative landscape. Practically, it provides a blueprint for constructing a quantum field theory of gravity without recourse to string theory or higher-dimensional conjectures.

Future Directions

In moving forward, CDT research has several promising directions. Efforts to enhance computational efficiency and measurement precision hold the potential to unlock deeper insights into the phase transitions and continuum limits. Furthermore, investigations into the inclusion of matter fields within the CDT framework remain relatively unexplored but are crucial for extending its applicability to real-world phenomena.

The potential for CDT to uncover evidence for asymptotic safety, or other nonperturbative UV completions, remains an exciting avenue. The search for new observables that could serve as reliable discriminants of universal quantum gravity properties will likely play a crucial role in determining the full scope of CDT’s applicability.

Overall, Causal Dynamical Triangulations presents a robust framework with critical implications for the theoretical conceptualization and computational evaluation of quantum gravity, holding promise for future exploration and discovery in the field of theoretical physics.