Numerical analysis of spin foam dynamics and the flatness problem

Abstract

In this paper, we apply a recently proposed numerical algorithm for finding stationary phase points in spin foam amplitudes. We study a spin foam amplitude with three vertices and a bulk face in 4d BF theory. We fix the boundary coherent states to three possible triangulations, one with zero deficit angle on the bulk face and two with non-zero deficit angle. We compute the amplitude numerically and we find a stationary phase point already at low spins in all the three cases. We comment on how this result contrasts with the claims of flatness problem in spin foam theories. We point out where these arguments may be misleading and we propose further computations to definitively answer the question.

arXiv comment15 pages, 5 + 2 figures. v3: Added section 7. Revised conclusions. Two more figures

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• Effective Spin Foam Models for Lorentzian Quantum Gravity
• Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity
• A high-performance code for EPRL spin foam amplitudes
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• Addendum: EPRL/FK Asymptotics and the Flatness Problem
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• Markov Chain Monte Carlo methods for graph refinement in Spinfoam Cosmology
• Spin-foams as semi-classical vertices: gluing constraints and a hybrid algorithm
• Summing bulk quantum numbers with Monte Carlo in spin foam theories
• Asymptotics of $\mathrm{SL}(2,\mathbb{C})$ coherent invariant tensors
• Numerical evaluation of spin foam amplitudes beyond simplices
• Radiative corrections to the Lorentzian EPRL spin foam propagator
• The accidental flatness constraint does not mean a wrong classical limit
• Spin foam amplitude of the black-to-white hole transition
• Experimental Simulation of Loop Quantum Gravity on a Photonic Chip
• A Monte Carlo algorithm for spin foam intertwiners
• A saddle-point finder and its application to the spin foam model
• A discretization of Holst's action for general relativity
• Loop quantum gravity with optimal control path integral, and application to black hole tunneling