Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects

Abstract

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.

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References in corpus (17)

• Nonperturbative Quantum Gravity
• Black hole evaporation: A paradigm
• The Real No-Boundary Wave Function in Lorentzian Quantum Cosmology
• The lifetime problem of evaporating black holes: mutiny or resignation
• Real-time Feynman path integral with Picard--Lefschetz theory and its applications to quantum tunneling
• Effective Spin Foam Models for Lorentzian Quantum Gravity
• Monte Carlo calculations of the finite density Thirring model
• The End of a Black Hole's Evaporation -- Part I
• Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator
• Discretization independence implies non-locality in 4D discrete quantum gravity
• Normalizing Flows and the Real-Time Sign Problem
• Worldvolume approach to the tempered Lefschetz thimble method
• Introductory Lectures on Quantum Cosmology (1990)
• Lorentzian quantum cosmology goes simplicial
• Complex Paths Around The Sign Problem
• Time-space duality in 2D quantum gravity
• Piecewise Flat Metrics and Quantum Gravity

Cited by in corpus (12)

• From spin foams to area metric dynamics to gravitons
• Towards effective actions for the continuum limit of spin foams
• Suppression of spacetime singularities in quantum gravity
• De Sitter horizon entropy from a simplicial Lorentzian path integral
• Lorentzian quantum cosmology from effective spin foams
• Tensor network approach to 2d Lorentzian quantum Regge calculus
• Spikes and spines in 4D Lorentzian simplicial quantum gravity
• Truly Lorentzian quantum cosmology
• Light ray fluctuations in simplicial quantum gravity
• Light ray fluctuation and lattice refinement of simplicial quantum gravity
• Causal structure and topology change in (2+1)-dimensional simplicial gravity
• Lorentzian quantum gravity via Pachner moves: one-loop evaluation