What is the Curvature of 2D Euclidean Quantum Gravity?

R. Loll; T. Niestadt

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arXiv · 2407.18120

What is the Curvature of 2D Euclidean Quantum Gravity?

R. Loll·T. Niestadt

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Abstract

We re-examine the nonperturbative curvature properties of two-dimensional Euclidean quantum gravity, obtained as the scaling limit of a path integral over dynamical triangulations of a two-sphere, which lies in the same universality class as Liouville quantum gravity. The diffeomorphism-invariant observable that allows us to compare the averaged curvature of highly quantum-fluctuating geometries with that of classical spaces is the so-called curvature profile. A Monte Carlo analysis on three geometric ensembles, which are physically equivalent but differ by the inclusion of local degeneracies, leads to new insights on the influence of finite-size effects. After eliminating them, we find strong evidence that the curvature profile of 2D Euclidean quantum gravity is best matched by that of a classical round four-sphere, rather than the five-sphere found in previous work. Our analysis suggests the existence of a well-defined quantum Ricci curvature in the scaling limit.

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R. Loll, T. Niestadt. 2024-07-25. What is the Curvature of 2D Euclidean Quantum Gravity?. https://arxiv.org/abs/2407.18120

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