The weak coupling limit of simplicial quantum gravity
Dec, 199832 pages
Published in:
- Nucl.Phys.B 550 (1999) 465-491
e-Print:
- hep-lat/9812022 [hep-lat]
Report number:
- BI-TH-98-38
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Abstract:
In the weak-coupling limit, kappa_0 going to infinity, the partition function of simplicial quantum gravity is dominated by an ensemble of triangulations with the ratio N_0/N_D close to the upper kinematic limit. For a combinatorial triangulation of the D--sphere this limit is 1/D. Defining an ensemble of maximal triangulations, i.e. triangulations that have the maximal possible number of vertices for a given volume, we investigate the properties of this ensemble in three dimensions using both Monte Carlo simulations and a strong-coupling expansion of the partition function, both for pure simplicial gravity and a with a suitable modified measure. For the latter we observe a continuous phase transition to a crinkled phase and we investigate the fractal properties of this phase.Note:
- 32 pages, latex2e + 17 eps files Report-no: BI-TP 98/38
- 04.60.-m
- 04.60.Nc
- 02.10.Eb
- quantum gravity: simplex
- partition function: measure
- approximation: weak coupling
- space-time: sphere
- triangulation
- dimension: 3
- expansion: strong coupling
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