Radiative corrections to the Lorentzian EPRL spin foam propagator

Abstract

We numerically estimate the divergence of several two-vertex diagrams that contribute to the radiative corrections for the Lorentzian EPRL spin foam propagator. We compute the amplitudes as functions of a homogeneous cutoff over the bulk quantum numbers, fixed boundary data, and different Immirzi parameters, and find that for a class of two-vertex diagrams, those with fewer than six internal faces are convergent. The calculations are done with the numerical framework sl2cfoam-next.

arXiv comment20 pages, 11 figures

References in corpus (32)

• The Spin Foam Approach to Quantum Gravity
• LQG vertex with finite Immirzi parameter
• Topological Lattice Models in Four Dimensions
• A New Spin Foam Model for 4d Gravity
• Group Field Theory: An overview
• Lorentzian spin foam amplitudes: graphical calculus and asymptotics
• Colored Group Field Theory
• Diffeomorphisms and spin foam models
• Spin-Foams for All Loop Quantum Gravity
• Decorated tensor network renormalization for lattice gauge theories and spin foam models
• Self-Energy of the Lorentzian EPRL-FK Spin Foam Model of Quantum Gravity
• Fast and accurate evaluation of Wigner 3j, 6j, and 9j symbols using prime factorisation and multi-word integer arithmetic
• Group field theory as the 2nd quantization of Loop Quantum Gravity
• Investigation of the Spinfoam Path integral with Quantum Cuboid Intertwiners
• Cosmological Constant in LQG Vertex Amplitude
• Melonic phase transition in group field theory
• Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity
• Boosting Wigner's nj-symbols
• A high-performance code for EPRL spin foam amplitudes
• Asymptotics of lowest unitary SL(2,C) invariants on graphs
• Bubble divergences: sorting out topology from cell structure
• Numerical analysis of spin foam dynamics and the flatness problem
• Discrete Symmetries in Covariant LQG
• Divergences and Orientation in Spinfoams
• How-To compute EPRL spin foam amplitudes
• Infrared divergences in the EPRL-FK Spin Foam model
• Numerical analysis of the self-energy in covariant Loop Quantum Gravity
• Renormalization of group field theories for quantum gravity: new scaling results and some suggestions
• Asymptotics of $\mathrm{SL}(2,\mathbb{C})$ coherent invariant tensors
• The accidental flatness constraint does not mean a wrong classical limit
• A finiteness bound for the EPRL/FK spin foam model
• Studying the EPRL spinfoam self-energy

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• Markov Chain Monte Carlo methods for graph refinement in Spinfoam Cosmology
• Summing bulk quantum numbers with Monte Carlo in spin foam theories
• Spinfoams: Foundations
• Spikes and spines in 4D Lorentzian simplicial quantum gravity
• Numerical approach to the black-to-white hole transition
• A Monte Carlo algorithm for spin foam intertwiners