https://doi.org/10.1140/epjc/s10052-024-13110-z
Regular Article - Theoretical Physics
Curvature correlators in nonperturbative 2D Lorentzian quantum gravity
1
Institute for Mathematics, Astrophysics and Particle Physics, Radboud University, Heyendaalseweg 135, 6525 AJ, Nijmegen, The Netherlands
2
Perimeter Institute for Theoretical Physics, 31 Caroline St N, N2L 2Y5, Waterloo, ON, Canada
Received:
29
April
2024
Accepted:
7
July
2024
Published online:
30
July
2024
Correlation functions are ubiquitous tools in quantum field theory from both a fundamental and a practical point of view. However, up to now their use in theories of quantum gravity beyond perturbative and asymptotically flat regimes has been limited, due to difficulties associated with diffeomorphism invariance and the dynamical nature of geometry. We present an analysis of a manifestly diffeomorphism-invariant, nonperturbative two-point curvature correlator in two-dimensional Lorentzian quantum gravity. It is based on the recently introduced quantum Ricci curvature and uses a lattice regularization of the full path integral in terms of causal dynamical triangulations. We discuss some of the subtleties and ambiguities in defining connected correlators in theories of dynamical geometry, and provide strong evidence from Monte Carlo simulations that the connected two-point curvature correlator in 2D Lorentzian quantum gravity vanishes. This work paves the way for an analogous investigation in higher dimensions.
© The Author(s) 2024
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