What is the curvature of 2D Euclidean quantum gravity?
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-inv...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-04-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP04(2025)158 |
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| Summary: | 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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| ISSN: | 1029-8479 |