Holonomy spin foam models: Asymptotic geometry of the partition function

Abstract

We study the asymptotic geometry of the spin foam partition function for a large class of models, including the models of Barrett and Crane, Engle, Pereira, Rovelli and Livine, and, Freidel and Krasnov. The asymptotics is taken with respect to the boundary spins only, no assumption of large spins is made in the interior. We give a sufficient criterion for the existence of the partition function. We find that geometric boundary data is suppressed unless its interior continuation satisfies certain accidental curvature constraints. This means in particular that most Regge manifolds are suppressed in the asymptotic regime. We discuss this explicitly for the case of the configurations arising in the 3-3 Pachner move. We identify the origin of these accidental curvature constraints as an incorrect twisting of the face amplitude upon introduction of the Immirzi parameter and propose a way to resolve this problem, albeit at the price of losing the connection to the SU(2) boundary Hilbert space. The key methodological innovation that enables these results is the introduction of the notion of wave front sets, and the adaptation of tools for their study from micro local analysis to the case of spin foam partition functions.

63 pages, 5 figures v2: Reference corrected

References in corpus (10)

• LQG vertex with finite Immirzi parameter
• A New Spin Foam Model for 4d Gravity
• The loop-quantum-gravity vertex-amplitude
• Flipped spinfoam vertex and loop gravity
• Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
• The Ponzano-Regge model
• New Action Principle for General Relativity
• Path integral representation of spin foam models of 4d gravity
• Operator Spin Foam Models
• Numerical evidence of regularized correlations in spin foam gravity

Cited by in corpus (44)

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• Effective Spin Foam Models for Lorentzian Quantum Gravity
• Numerical study of the Lorentzian Engle-Pereira-Rovelli-Livine spin foam amplitude
• Investigation of the Spinfoam Path integral with Quantum Cuboid Intertwiners
• SU(2) graph invariants, Regge actions and polytopes
• Numerical methods for EPRL spin foam transition amplitudes and Lorentzian recoupling theory
• Boosting Wigner's nj-symbols
• A high-performance code for EPRL spin foam amplitudes
• Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime
• Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator
• Asymptotics of lowest unitary SL(2,C) invariants on graphs
• Discrete gravity dynamics from effective spin foams
• Numerical analysis of spin foam dynamics and the flatness problem
• Asymptotic analysis of the EPRL model with timelike tetrahedra
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity II - From coherent quantum boundaries to BMS3 characters
• Einstein Equation from Covariant Loop Quantum Gravity in Semiclassical Continuum Limit
• Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
• Addendum: EPRL/FK Asymptotics and the Flatness Problem
• From spin foams to area metric dynamics to gravitons
• Towards effective actions for the continuum limit of spin foams
• Searching for classical geometries in spin foam amplitudes: a numerical method
• EPRL/FK Asymptotics and the Flatness Problem
• Emergent 4-dimensional linearized gravity from spin foam model
• A note on the secondary simplicity constraints in loop quantum gravity
• Twisted geometries, twistors and conformal transformations
• Quantum geometry from higher gauge theory
• On Spinfoams Near a Classical Curvature Singularity
• Spin-foams as semi-classical vertices: gluing constraints and a hybrid algorithm
• Spinfoams and high performance computing
• Numerical evaluation of spin foam amplitudes beyond simplices
• Twisted geometries are area-metric geometries
• The accidental flatness constraint does not mean a wrong classical limit
• Spinfoams: Foundations
• The Barrett-Crane model: asymptotic measure factor
• Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data
• Curvature effects in the spectral dimension of spin foams
• Semiclassical Behavior of Spinfoam Amplitude with Small Spins and Entanglement Entropy
• A Monte Carlo algorithm for spin foam intertwiners
• Loop quantum gravity, twistors, and some perspectives on the problem of time
• A Wick rotation for EPRL spin foam models
• Geometry from local flatness in Lorentzian spin foam theories
• A simpler way of imposing simplicity constraints
• Radiative corrections to the EPRL-FK spinfoam graviton
• The hessian in spin foam models