2021/10/31 by Ding Jia
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Euclidean quantum gravity #Gravitation #Holomorphic function #Loop quantum gravity #Mathematical analysis #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Simplicial complex #Simplicial manifold #Spin foam #Theoretical physics #gr-qc #hep-lat #hep-th
paper · pdf · doi:10.1088/1361-6382/ac4b04
published as Class. Quantum Grav. 39, 065002 (2022) · matches well published version
openalex publication_date 2022/01/13 · arxiv created 2022/03/01 · arxiv updated 2022/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Evaluating gravitational path integrals in the Lorentzian has been a long-standing challenge due to the numerical sign problem. We show that this challenge can be overcome in simplicial quantum gravity. By deforming the integration contour into the complex, the sign fluctuations can be suppressed, for instance using the holomorphic gradient flow algorithm. Working through simple models, we show that this algorithm enables efficient Monte Carlo simulations for Lorentzian simplicial quantum gravity. In order to allow complex deformations of the integration contour, we provide a manifestly holomorphic formula for Lorentzian simplicial gravity. This leads to a complex version of simplicial gravity that generalizes the Euclidean and Lorentzian cases. Outside the context of numerical computation, complex simplicial gravity is also relevant to studies of singularity resolving processes with complex semi-classical solutions. Along the way, we prove a complex version of the Gauss-Bonnet theorem, which may be of independent interest.