Scaling in quantum gravity

Ambjørn, J.; Watabiki, Yoshiyuki

doi:10.1016/0550-3213(95)00154-k

Cited by 153 publications

(253 citation statements)

References 25 publications

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“…We recognize that the lattice triangulation version of S A (R) corresponds to s N (r). According to the numerical result, we expect to have a relation In case of pure gravity (c = 0) S A (R) was calculated analytically 20) where f (x) ∼ e −x 4/3 for large x [9,14]. This analytic result is consistent with the calculation of the fractal dimension d F = 4 for c = 0 model derived by transfer matrix formalism [7].…”

Section: The Fractal Dimensionsupporting

confidence: 82%

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Numerical study for the c-dependence of fractal dimension in two-dimensional quantum gravity

Kawamoto

Yotsuji

2002

Nuclear Physics B

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We numerically investigate the fractal structure of two-dimensional quantum gravity coupled to matter central charge c for −2 ≤ c ≤ 1. We reformulate Q-state Potts model into the model which can be identified as a weighted percolation cluster model and can make continuous change of Q, which relates c, on the dynamically triangulated lattice. The c-dependence of the critical coupling is measured from the percolation probability and susceptibility. The c-dependence of the string susceptibility of the quantum surface is evaluated and has very good agreement with the theoretical predictions. The c-dependence of the fractal dimension based on the finite size scaling hypothesis is measured and has excellent agreement with one of the theoretical predictions previously proposed except for the region near c ≈ 1.

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Section: The Fractal Dimensionsupporting

confidence: 82%

“…It has then been recognized that two point function of random surface can be related to the measurement of s N (r) [9,14,43]. In the case of pure gravity (c = 0) "two-point function" with fixed volume A is defined by…”

Section: The Fractal Dimensionmentioning

confidence: 99%

Numerical study for the c-dependence of fractal dimension in two-dimensional quantum gravity

Kawamoto

Yotsuji

2002

Nuclear Physics B

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“…Still, some results were obtained in Refs. [6][7][8], where in particular combinatorial arguments were used to derive the universal scaling two-point function for critical genus zero surfaces with two marked points at a fixed geodesic distance. However, an explicit form for the two-point function was obtained only in the pure gravity case and close to the critical point.…”

Section: Introductionmentioning

confidence: 99%

Geodesic distance in planar graphs

2003

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We derive the exact generating function for planar maps (genus zero fatgraphs) with vertices of arbitrary even valence and with two marked points at a fixed geodesic distance. This is done in a purely combinatorial way based on a bijection with decorated trees, leading to a recursion relation on the geodesic distance. The latter is solved exactly in terms of discrete soliton-like expressions, suggesting an underlying integrable structure. We extract from this solution the fractal dimensions at the various (multi)-critical points, as well as the precise scaling forms of the continuum two-point functions and the probability distributions for the geodesic distance in (multi)-critical random surfaces. The two-point functions are shown to obey differential equations involving the residues of the KdV hierarchy. 03/031

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“…(4). As shown in [9,16] an object like G 1 (R; Λ) is a good probe of the fractal structure of space-time which is determined by the exponential decay of G 1 (R; Λ). We expect…”

Section: Introductionmentioning

confidence: 99%