Spinfoam on a Lefschetz thimble: Markov chain Monte Carlo computation of a Lorentzian spinfoam propagator

Abstract

We compute numerically the Lorentzian Engle-Pereira-Rovelli-Livine spinfoam propagator on a 4-simplex, by adapting the Lefschetz thimble and Markov chain Monte-Carlo methods 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 semiclassical 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 semiclassical and quantum behaviors of the spinfoam model.