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

2021; American Physical Society; Volume: 103; Issue: 8 Linguagem: Inglês

10.1103/physrevd.103.084026

2470-0037

Muxin Han, Zichang Huang, Hongguang Liu, Dongxue Qu, Yidun Wan,

Black Holes and Theoretical Physics

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.