Dynamically Triangulating Lorentzian Quantum Gravity

Abstract

Fruitful ideas on how to quantize gravity are few and far between. In this paper, we give a complete description of a recently introduced non-perturbative gravitational path integral whose continuum limit has already been investigated extensively in d less than 4, with promising results. It is based on a simplicial regularization of Lorentzian space-times and, most importantly, possesses a well-defined, non-perturbative Wick rotation. We present a detailed analysis of the geometric and mathematical properties of the discretized model in d=3,4. This includes a derivation of Lorentzian simplicial manifold constraints, the gravitational actions and their Wick rotation. We define a transfer matrix for the system and show that it leads to a well-defined self-adjoint Hamiltonian. In view of numerical simulations, we also suggest sets of Lorentzian Monte Carlo moves. We demonstrate that certain pathological phases found previously in Euclidean models of dynamical triangulations cannot be realized in the Lorentzian case.

41 pages, 14 figures

References in corpus (1)

• A proper-time cure for the conformal sickness in quantum gravity

Cited by in corpus (194)

• The nonperturbative functional renormalization group and its applications
• Gravity's Rainbow
• Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation
• Spectral Dimension of the Universe
• Emergence of a 4D World from Causal Quantum Gravity
• Reconstructing the Universe
• Nonperturbative Quantum Gravity
• Flow Equation of Quantum Einstein Gravity in a Higher-Derivative Truncation
• Quantum Gravity from Causal Dynamical Triangulations: A Review
• Fractal Spacetime Structure in Asymptotically Safe Gravity
• Ultraviolet properties of f(R)-Gravity
• The Asymptotic Safety Scenario in Quantum Gravity -- An Introduction
• Cosmology of the Lifshitz universe
• Planckian Birth of the Quantum de Sitter Universe
• The Nonperturbative Quantum de Sitter Universe
• Melons are branched polymers
• The Universe from Scratch
• Quantum Gravity at Astrophysical Distances?
• En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions
• Spectral geometry as a probe of quantum spacetime
• Proper Time Flow Equation for Gravity
• Higher Derivative Quantum Gravity with Gauss-Bonnet Term
• Ghost anomalous dimension in asymptotically safe quantum gravity
• Semiclassical Universe from First Principles
• A second-order phase transition in CDT
• A proper-time cure for the conformal sickness in quantum gravity
• CDT meets Horava-Lifshitz gravity
• Triply Special Relativity
• Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates
• The universe as a quantum gravity condensate
• Quantum gravity and Standard-Model-like fermions
• (Broken) Gauge Symmetries and Constraints in Regge Calculus
• Second- and First-Order Phase Transitions in CDT
• The Semiclassical Limit of Causal Dynamical Triangulations
• Non-perturbative summation over 3D discrete topologies
• Lattice Quantum Gravity and Asymptotic Safety
• Quantizing Horava-Lifshitz Gravity via Causal Dynamical Triangulations
• Canonical quantization of general relativity in discrete space-times
• Effective Spin Foam Models for Lorentzian Quantum Gravity
• A String Field Theory based on Causal Dynamical Triangulations
• Renormalization Group Flow in CDT
• Quantum gravity and the standard model
• Asymptotically Safe Cosmology
• Quantum Gravity via Causal Dynamical Triangulations
• Loop and spin foam quantum gravity: a brief guide for beginners
• The Emergence of Spacetime, or, Quantum Gravity on Your Desktop
• A Matrix Model for 2D Quantum Gravity defined by Causal Dynamical Triangulations
• Towards a double-scaling limit for tensor models: probing sub-dominant orders
• Renormalization and asymptotic safety in truncated quantum Einstein gravity
• A Lorentzian cure for Euclidean troubles
• Quantum gravity as sum over spacetimes
• Black hole image encoding quantum gravity information
• Black Holes and Covariance in Effective Quantum Gravity
• Shaken, but not stirred - Potts model coupled to quantum gravity
• Absorption, Scattering, Geodesics, Shadows and Lensing Phenomena of Black Holes in Effective Quantum Gravity
• Counting a black hole in Lorentzian product triangulations
• Characteristics of the new phase in CDT
• Putting a cap on causality violations in CDT
• Geometry of the quantum universe
• Euclidian 4d quantum gravity with a non-trivial measure term
• Asymptotic analysis of spin foam amplitude with timelike triangles
• De Sitter Universe from Causal Dynamical Triangulations without Preferred Foliation
• Constraints on rainbow gravity functions from black hole thermodynamics
• (2+1)-Dimensional Quantum Gravity as the Continuum Limit of Causal Dynamical Triangulations
• Gravitational lensing effect of black holes in effective quantum gravity
• The effective action in 4-dim CDT. The transfer matrix approach
• Spin foams with timelike surfaces
• Impact of topology in causal dynamical triangulations quantum gravity
• Stochastic quantization and the role of time in quantum gravity
• Symmetry and Evolution in Quantum Gravity
• Trees and spatial topology change in CDT
• Statistical Mechanics of Graphity Models
• The phase structure of Causal Dynamical Triangulations with toroidal spatial topology
• Spacetime condensation in (2+1)-dimensional CDT from a Horava-Lifshitz minisuperspace model
• Extensions of Lorentzian spacetime geometry: From Finsler to Cartan and vice versa
• Renormalization of 3d quantum gravity from matrix models
• The emergence of background geometry from quantum fluctuations
• The moduli space of isometry classes of globally hyperbolic spacetimes
• Quantum gravity on a square graph
• Renormalisation group improvement of scalar field inflation
• Universal critical behavior in tensor models for four-dimensional quantum gravity
• Four-dimensional CDT with toroidal topology
• Induced Spatial Geometry from Causal Structure
• Towards a $C$-function in 4D quantum gravity
• A Monte-Carlo study of the AdS/CFT correspondence: an exploration of quantum gravity effects
• A Hexagon Model for 3D Lorentzian Quantum Cosmology
• Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model
• The de Sitter Instanton from Euclidean Dynamical Triangulations
• The transfer matrix in four-dimensional CDT
• Suppression of non-manifold-like sets in the causal set path integral
• Quantum cosmology and eternal inflation
• Quantum Gravity and Matter: Counting Graphs on Causal Dynamical Triangulations
• Effective dynamics of scalar cosmological perturbations from quantum gravity
• A discrete history of the Lorentzian path integral
• A Validation of Causal Dynamical Triangulations
• Searching for a continuum limit in causal dynamical triangulation quantum gravity
• Fixed-Topology Lorentzian Triangulations: Quantum Regge Calculus in the Lorentzian Domain
• Quantum Riemannian geometry and particle creation on the integer line
• Towards background independent quantum gravity with tensor models
• Quantum gravity as a Fermi liquid
• Dynamical dimensional reduction in toy models of 4D causal quantum gravity
• Cosmic string in gravity's rainbow
• Black holes and covariance in effective quantum gravity: A solution without Cauchy horizons
• Thermodynamics of Reissner-Nordström Black Holes in Higher Dimensions: Rainbow Gravity Background With General Uncertainty Principle
• Realizability of the Lorentzian (n,1)-Simplex
• Taming the cosmological constant in 2D causal quantum gravity with topology change
• Pseudo-topological transitions in 2D gravity models coupled to massless scalar fields
• Spectroscopy of a canonically quantized horizon
• A first look at transition amplitudes in (2+1)-dimensional causal dynamical triangulations
• Quantum field theory on a growing lattice
• The Self-Organized de Sitter Universe
• The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization
• Towards an UV fixed point in CDT gravity
• Locally Causal Dynamical Triangulations in Two Dimensions
• Wilson loops in CDT quantum gravity
• The Spectral Geometry of de Sitter Space in Asymptotic Safety
• CDT and Cosmology
• Asymptotic safety on the lattice: The Nonlinear O(N) Sigma Model
• Coupling a Point-Like Mass to Quantum Gravity with Causal Dynamical Triangulations
• Relating Covariant and Canonical Approaches to Triangulated Models of Quantum Gravity
• Quantum gravity on polygons and $\mathbb{R}\times {\mathbb{Z}}_n$ FLRW model
• Renormalization of lattice-regularized quantum gravity models II. The case of causal dynamical triangulations
• A quantization of topological M theory
• Exploring Torus Universes in Causal Dynamical Triangulations
• Gauge fixing in Causal Dynamical Triangulations
• Fuzzy and discrete black hole models
• Scale-dependent homogeneity measures for causal dynamical triangulations
• Lorentzian quantum cosmology from effective spin foams
• Quantum Flatness in Two-Dimensional CDT Quantum Gravity
• Continuum interpretation of the dynamical-triangulation formulation of quantum Einstein gravity
• The higher-order phase transition in toroidal CDT
• Models of the Universe based on Jordan algebras
• Causal Dynamical Triangulations in Four Dimensions
• Reconstructing the graviton
• Discrete Gravity
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• A causal perspective on random geometry
• Quantum widening of CDT universe
• Spin foam amplitude of the black-to-white hole transition
• Critical Phenomena in Causal Dynamical Triangulations
• Renormalization group flow of coupled tensorial group field theories: Towards the Ising model on random lattices
• Curved domain-wall fermions
• The microscopic structure of 2D CDT coupled to matter
• Classical and quantum $f(R)$ cosmology: The big rip, the little rip and the little sibling of the big rip
• Capturing the phase diagram of (2+1)-dimensional CDT using a balls-in-boxes model
• Spinfoams: Foundations
• Scalar fields in Causal Dynamical Triangulations
• A c=1 phase transition in two-dimensional CDT/Horava-Lifshitz gravity?
• Properties of dynamical fractal geometries in the model of Causal Dynamical Triangulations
• Quantizations of D=3 Lorentz symmetry
• Minimizers of the dynamical Boulatov model
• Measuring the Homogeneity (or Otherwise) of the Quantum Universe
• Universality of 2d causal dynamical triangulations
• Is Lattice Quantum Gravity Asymptotically Safe? Making contact between Causal Dynamical Triangulations and the Functional Renormalization Group
• A statistical formalism of Causal Dynamical Triangulations
• Foliations and 2+1 Causal Dynamical Triangulation Models
• Network Gravity
• Thermodynamic phase transition and Joule-Thomson expansion of a quantum corrected black hole in AdS spacetime
• Rainbow Rindler metric and Unruh effect
• The spectral dimension in 2D CDT gravity coupled to scalar fields
• Extracting Geometry from Quantum Spacetime: Obstacles down the road
• Scaling analyses of the spectral dimension in 3-dimensional causal dynamical triangulations
• Setting the physical scale of dimensional reduction in causal dynamical triangulations
• Regarding the `Hole Argument' and the `Problem of Time'
• Entanglement entropy on finitely ramified graphs
• The phase structure and effective action of 3D CDT at higher spatial genus
• $\Psi$-Epistemic Quantum Cosmology?
• Quantum Topology Change and Large N Gauge Theories
• A second look at transition amplitudes in (2+1)-dimensional causal dynamical triangulations
• Collisions in piecewise flat gravity in 3+1 dimensions
• Functional approach to 2+1 dimensional gravity coupled to particles
• Compact Gauge Fields on Causal Dynamical Triangulations: a 2D case study
• Quantum Riemannian geometry of the discrete interval and q-deformation
• 10 D Euclidean dynamical triangulations
• Geometry-Information Duality: Quantum Entanglement Contributions to Gravitational Dynamics
• On the Nature of Spatial Universes in 3D Lorentzian Quantum Gravity
• Proper time is stochastic time in 2d quantum gravity
• Asymptotic safety and quantum gravity amplitudes
• Towards elucidation of zero-temperature criticality of Ising model on 2d DT
• Spectral dimension in graph models of causal quantum gravity
• Phase transitions in TGFT: Landau-Ginzburg analysis of the causally complete Lorentzian Barrett-Crane model
• The Repulsive Effect of Covariant Effective Quantum Gravity
• Shadow constraints of charged black hole with scalar hair and gravitational waves from extreme mass ratio inspirals
• Causal dynamical triangulation of a 3D tensor model
• Scaling-Based Quantization of Spacetime Microstructure
• Matters of Gravity, the newsletter of the APS Topical Group on Gravitation, Spring 2001
• World quantum gravity: Quantum test objects and Synge's world function
• On rips and cosmological singularities in a universe merging with baby universes
• Rotationally invariant dynamical lattice regulators for Euclidean quantum field theories
• Making the case for causal dynamical triangulations
• Landau Theory of Causal Dynamical Triangulations
• Triangulations of Conal Manifolds
• 10 D Euclidean quantum gravity on the lattice
• CDT open-closed surface field theory of a 3D tensor-matrix model