4D Quantum Gravity Coupled to Matter

Abstract

We investigate the phase structure of four-dimensional quantum gravity coupled to Ising spins or Gaussian scalar fields by means of numerical simulations. The quantum gravity part is modelled by the summation over random simplicial manifolds, and the matter fields are located in the center of the 4-simplices, which constitute the building blocks of the manifolds. We find that the coupling between spin and geometry is weak away from the critical point of the Ising model. At the critical point there is clear coupling, which qualitatively agrees with that of gaussian fields coupled to gravity. In the case of pure gravity a transition between a phase with highly connected geometry and a phase with very ``dilute'' geometry has been observed earlier. The nature of this transition seems unaltered when matter fields are included. It was the hope that continuum physics could be extracted at the transition between the two types of geometries. The coupling to matter fields, at least in the form discussed in this paper, seems not to improve the scaling of the curvature at the transition point.

15 pages, 9 figures (available as PS-files by request). Latex

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Cited by in corpus (14)

• Nonperturbative Quantum Gravity
• Discrete approaches to quantum gravity in four dimensions
• Functional Integration Over Geometries
• Scaling in four dimensional quantum gravity
• Group field theory for quantum gravity minimally coupled to a scalar field
• Kähler-Dirac fermions on Euclidean dynamical triangulations
• CDT---an Entropic Theory of Quantum Gravity
• Gravitational binding in 4D dynamical triangulation
• Dynamical Triangulations, a Gateway to Quantum Gravity ?
• Coupling a Point-Like Mass to Quantum Gravity with Causal Dynamical Triangulations
• Ising-link Quantum Gravity
• Scalar fields in Causal Dynamical Triangulations
• Simplicial Quantum Gravity on a Computer
• Emergence of gravity from interacting simplices