Asymptotic freedom and Euclidean quantum gravity. (English) Zbl 1043.83528
Summary: Pure SU(2) gauge theory is the simplest asymptotically free theory in four dimensions. To investigate the possibility that the entropy dominated region in euclidean quantum gravity is of physical relevance, we simulate \(4d\) SU(2) lattice gauge theory on a dynamically coupled Regge skeleton. The fluctuations of the skeleton are governed by the standard Regge-Einstein action. From a small 2x4\(^3\) lattice we report exploratory numerical results, limited to a region of strong gravity where the Planck mass and hadronic masses take similar orders of magnitude. We find a range of the Planck mass where stable bulk expectation values are obtained which vary smoothly with the gauge coupling, and a remnant of the QCD deconfining phase transition is located. For a consistent picture of quantum gravity coupled with an asymptotically free field theory a necessary, but not sufficient, condition is to observe a scaling law in future simulations.
MSC:
| 83C45 | Quantization of the gravitational field |
| 83C27 | Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory |
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