Scaling and the fractal geometry of two-dimensional quantum gravity

S. Catterall; G. Thorleifsson; M. Bowick; V. John

doi:10.1016/0370-2693(95)00623-S

Scaling and the fractal geometry of two-dimensional quantum gravity

S. Catterall, G. Thorleifsson, M. Bowick, V. John

Department of Physics

Research output: Contribution to journal › Article › peer-review

45 Scopus citations

Abstract

We examine the scaling of geodesic correlation functions in two-dimensional gravity and in spin systems coupled to gravity. The numerial data support the scaling hypothesis and indicate that the quantum geometry develops a non-perturbative length scale. The existence of this length scale allows us to extract a Hausdorff dimension. In the case of pure gravity we find d_H ≈ 3.8, in support of recent theoretical calculations that d_H = 4. We also discuss the back-reaction of matter on the geometry.

Original language	English (US)
Pages (from-to)	58-68
Number of pages	11
Journal	Physics Letters B
Volume	354
Issue number	1-2
DOIs	https://doi.org/10.1016/0370-2693(95)00623-S
State	Published - Jul 13 1995

ASJC Scopus subject areas

Nuclear and High Energy Physics

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title = "Scaling and the fractal geometry of two-dimensional quantum gravity",

abstract = "We examine the scaling of geodesic correlation functions in two-dimensional gravity and in spin systems coupled to gravity. The numerial data support the scaling hypothesis and indicate that the quantum geometry develops a non-perturbative length scale. The existence of this length scale allows us to extract a Hausdorff dimension. In the case of pure gravity we find dH ≈ 3.8, in support of recent theoretical calculations that dH = 4. We also discuss the back-reaction of matter on the geometry.",

author = "S. Catterall and G. Thorleifsson and M. Bowick and V. John",

note = "Funding Information: This researchw as supportedb y the Department of Energy, USA, under contract No. DE-FGOZ 85ER40237a nd by researchf unds from Syracuse University.W e would also like to acknowledgeth e useo f NPAC computationfaal cilitiesa ndt hev aluable helpo f Marco Falcioni.",

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T1 - Scaling and the fractal geometry of two-dimensional quantum gravity

AU - Catterall, S.

AU - Thorleifsson, G.

AU - Bowick, M.

AU - John, V.

N1 - Funding Information: This researchw as supportedb y the Department of Energy, USA, under contract No. DE-FGOZ 85ER40237a nd by researchf unds from Syracuse University.W e would also like to acknowledgeth e useo f NPAC computationfaal cilitiesa ndt hev aluable helpo f Marco Falcioni.

PY - 1995/7/13

Y1 - 1995/7/13

N2 - We examine the scaling of geodesic correlation functions in two-dimensional gravity and in spin systems coupled to gravity. The numerial data support the scaling hypothesis and indicate that the quantum geometry develops a non-perturbative length scale. The existence of this length scale allows us to extract a Hausdorff dimension. In the case of pure gravity we find dH ≈ 3.8, in support of recent theoretical calculations that dH = 4. We also discuss the back-reaction of matter on the geometry.

AB - We examine the scaling of geodesic correlation functions in two-dimensional gravity and in spin systems coupled to gravity. The numerial data support the scaling hypothesis and indicate that the quantum geometry develops a non-perturbative length scale. The existence of this length scale allows us to extract a Hausdorff dimension. In the case of pure gravity we find dH ≈ 3.8, in support of recent theoretical calculations that dH = 4. We also discuss the back-reaction of matter on the geometry.

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Scaling and the fractal geometry of two-dimensional quantum gravity

Abstract

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