Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator

Abstract

We compute numerically the Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam propagator on a 4-simplex, by adapting the methods of Lefschetz thimble and Markov Chain Monte-Carlo to oscillatory spinfoam integrals. Our method can compute any spinfoam observables at relatively large spins. We obtain the numerical results of the propagators at different spins and demonstrate their consistency with the expected spinfoam semi-classical behavior in the large spin limit. Our results exhibit significant quantum corrections at smaller spins. Our method is reliable and thus can be employed to discover the semi-classical and quantum behaviors of the spinfoam model.

arXiv comment26 pages, 8 figures, 11 tables

References in corpus (54)

• MCMC using Hamiltonian dynamics
• Background Independent Quantum Gravity: A Status Report
• LQG vertex with finite Immirzi parameter
• Spin Foam Models for Quantum Gravity
• A New Spin Foam Model for 4d Gravity
• High density QCD on a Lefschetz thimble?
• Analytic Continuation Of Chern-Simons Theory
• Fundamental Structure of Loop Quantum Gravity
• Lorentzian spin foam amplitudes: graphical calculus and asymptotics
• On the semiclassical limit of 4d spin foam models
• Graviton propagator from background-independent quantum gravity
• Holomorphic Blocks in Three Dimensions
• LQG propagator from the new spin foams
• A Monte Carlo algorithm for simulating fermions on Lefschetz thimbles
• A new approach to the complex-action problem and its application to a nonperturbative study of superstring theory
• General boundary quantum field theory: Foundations and probability interpretation
• Numerical evidence for a phase transition in 4d spin foam quantum gravity
• Spin foam models for quantum gravity from lattice path integrals
• Lefschetz-thimble analysis of the sign problem in one-site fermion model
• Structure of Lefschetz thimbles in simple fermionic systems
• SL(2,C) Chern-Simons Theory, a non-Planar Graph Operator, and 4D Loop Quantum Gravity with a Cosmological Constant: Semiclassical Geometry
• Lorentzian spinfoam propagator
• Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory
• Numerical study of the Lorentzian Engle-Pereira-Rovelli-Livine spin foam amplitude
• Deep Learning Beyond Lefschetz Thimbles
• Quantum gravity asymptotics from the SU(2) 15j symbol
• Holonomy spin foam models: Asymptotic geometry of the partition function
• Generalized Spinfoams
• Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory
• Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
• Numerical methods for EPRL spin foam transition amplitudes and Lorentzian recoupling theory
• Four-dimensional Quantum Gravity with a Cosmological Constant from Three-dimensional Holomorphic Blocks
• Lefschetz thimbles decomposition for the Hubbard model on the hexagonal lattice
• Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime
• Numerical evidence of regularized correlations in spin foam gravity
• On Spinfoam Models in Large Spin Regime
• Asymptotics of lowest unitary SL(2,C) invariants on graphs
• Path Integral Representation of Lorentzian Spinfoam Model, Asymptotics, and Simplicial Geometries
• Towards the graviton from spinfoams: the 3d toy model
• Numerical analysis of spin foam dynamics and the flatness problem
• Asymptotic analysis of spin foam amplitude with timelike triangles
• Finite Density $QE{D}_{1+1}$ Near Lefschetz Thimbles
• Asymptotic analysis of the EPRL model with timelike tetrahedra
• Probing Loop Quantum Gravity with Evaporating Black Holes
• Euclidean three-point function in loop and perturbative gravity
• A complex path around the sign problem
• 4d Quantum Geometry from 3d Supersymmetric Gauge Theory and Holomorphic Block
• Emergence of Spacetime in a restricted Spin-foam model
• Emergent 4-dimensional linearized gravity from spin foam model
• Numerical computations of next-to-leading order corrections in spinfoam large-$j$ asymptotics
• Sub-leading asymptotic behaviour of area correlations in the Barrett-Crane model
• Analytic Continuation of Spin foam Models
• Reweighting Lefschetz Thimbles
• Spin foam propagator: A new perspective to include a cosmological constant

Cited by in corpus (30)

• A Short Review of Loop Quantum Gravity
• Effective Spin Foam Models for Lorentzian Quantum Gravity
• A high-performance code for EPRL spin foam amplitudes
• How-To compute EPRL spin foam amplitudes
• From spin foams to area metric dynamics to gravitons
• Towards effective actions for the continuum limit of spin foams
• Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects
• Analytic Continuation of Spin foam Models
• Complex critical points in Lorentzian spinfoam quantum gravity: 4-simplex amplitude and effective dynamics on double-${\Delta }_3$ complex
• Numerical analysis of the self-energy in covariant Loop Quantum Gravity
• Spin-foams as semi-classical vertices: gluing constraints and a hybrid algorithm
• Markov Chain Monte Carlo methods for graph refinement in Spinfoam Cosmology
• Summing bulk quantum numbers with Monte Carlo in spin foam theories
• Spinfoams and high performance computing
• Numerical evaluation of spin foam amplitudes beyond simplices
• Lorentzian quantum cosmology from effective spin foams
• Spinfoams: Foundations
• Finiteness of spinfoam vertex amplitude with timelike polyhedra, and the full amplitude
• Numerical approach to the black-to-white hole transition
• Towards quantum gravity with neural networks: Solving the quantum Hamilton constraint of U(1) BF theory
• Cosmology in Lorentzian Regge calculus: causality violations, massless scalar field and discrete dynamics
• Curvature effects in the spectral dimension of spin foams
• Toward matter dynamics in spin foam quantum gravity
• A Wick rotation for EPRL spin foam models
• A Monte Carlo algorithm for spin foam intertwiners
• Towards quantum gravity with neural networks: Solving quantum Hamilton constraints of 3d Euclidean gravity in the weak coupling limit
• Expansion operators in spherically symmetric loop quantum gravity
• Spinfoam tunneling of quantum geometries in angle variables
• A discretization of Holst's action for general relativity
• A saddle-point finder and its application to the spin foam model