Scaling in quantum gravity
نویسنده
چکیده
The 2-point function is the natural object in quantum gravity for extracting critical behavior: The exponential fall off of the 2-point function with geodesic distance determines the fractal dimension dH of space-time. The integral of the 2-point function determines the entropy exponent γ, i.e. the fractal structure related to baby universes, while the short distance behavior of the 2-point function connects γ and dH by a quantum gravity version of Fisher’s scaling relation. We verify this behavior in the case of 2d gravity by explicit calculation.
منابع مشابه
Scaling Dimensions of Manifestly Generally Covariant Operators in Two-Dimensional Quantum Gravity
Using (2+ǫ)-dimensional quantum gravity recently formulated by Kawai, Kitazawa and Ninomiya, we calculate the scaling dimensions of manifestly generally covariant operators in two-dimensional quantum gravity coupled to (p, q) minimal conformal matter. Although the spectrum includes all the scaling dimensions of the scaling operators in the matrix model except the boundary operators, there are a...
متن کاملFractal Quantum Space -Time
In this paper we calculated the spectral dimension of loop quantum gravity (LQG) using the scaling property of the area operator spectrum on spin-network states and using the scaling property of the volume and length operators on Gaussian states. We obtained that the spectral dimension of the spatial section runs from 1.5 to 3, and under particular assumptions from 2 to 3 across a 1.5 phase whe...
متن کاملScaling and the Fractal Geometry of Two-Dimensional Quantum Gravity
We examine the scaling of geodesic correlation functions in two-dimensional gravity and in spin systems coupled to gravity. The numerical data support the scaling hypothesis and indicate that the quantum geometry develops a nonperturbative 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 rece...
متن کاملCritical Behavior of Dynamically Triangulated Quantum Gravity in Four Dimensions
We performed detailed study of the phase transition region in Four Dimensional Simplicial Quantum Gravity, using the dynamical triangulation approach. The phase transition between the Gravity and Antigravity phases turned out to be asymmetrical, so that we observed the scaling laws only when the Newton constant approached the critical value from perturbative side. The curvature susceptibility d...
متن کامل3 D Lorentzian Quantum Gravity from the asymmetric ABAB matrix model 1
The asymmetric ABAB-matrix model describes the transfer matrix of threedimensional Lorentzian quantum gravity. We study perturbatively the scaling of the ABAB-matrix model in the neighbourhood of its symmetric solution and deduce the associated renormalization of three-dimensional Lorentzian quantum gravity. pacs: 04.60Gw, 04.20Gz, 04.60Kz, 04.60Nc Presented by J.J. at the Workshop on Random Ge...
متن کاملGround State of 2d Quantum Gravity and Spectral Density of Random Matrices
We compute the exact spectral density of random matrices in the ground state of the quantum hamiltonian corresponding to the matrix model whose double scaling limit describes pure gravity in 2D. We show that the non-perturbative effects are very large and in certain cases dominate the semi-classical WKB contribution studied in the earlier literature. The physical observables in this model are t...
متن کامل