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

TL;DR

This paper introduces a numerical method combining Lefschetz thimble and Markov Chain Monte-Carlo techniques to compute Lorentzian spinfoam propagators, revealing semi-classical limits and quantum corrections.

Contribution

It adapts advanced numerical methods to compute spinfoam propagators at large spins, enabling exploration of semi-classical and quantum regimes in Lorentzian spinfoam models.

Findings

Propagators match semi-classical behavior at large spins

Quantum corrections are significant at smaller spins

Method reliably computes spinfoam observables

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.