On the fractal structure of two-dimensional quantum gravity
J. Ambjorn, J. Jurkiewicz, Y. Watabiki (Niels Bohr Institute)
TL;DR
This paper investigates the fractal geometry of two-dimensional quantum gravity coupled with matter, revealing how the Hausdorff and spectral dimensions vary with the matter's central charge.
Contribution
It provides evidence for the specific fractal dimensions of 2D quantum gravity across different matter central charges, extending understanding of its geometric properties.
Findings
Hausdorff dimension is 4 for c ≤ 1
Spectral dimension is 2 for c ≤ 1
Dimensions decrease to 2 and 1 respectively for c > 1
Abstract
We provide evidence that the Hausdorff dimension is 4 and the spectral dimension is 2 for two-dimensional quantum gravity coupled the matter with a central charge . For the Hausdorff dimension and the spectral dimension monotonously decreases to 2 and 1, respectively.
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