Three-dimensional simplicial gravity and combinatorics of group presentations

Details Three-dimensional simplicial gravity and combinatorics of group presentations Three-dimensional simplicial gravity and combinatorics of group presentations

1998-04-10

arxiv.org/abs/hep-th/9804078v1

JHEP 9807:010,1998

Physics

High Energy Physics

High Energy Physics - Theory

24 pages

Scientific paper

10.1088/1126-6708/1998/07/010

We demonstrate how some problems arising in simplicial quantum gravity can be successfully addressed within the framework of combinatorial group theory. In particular, we argue that the number of simplicial 3-manifolds having a fixed homology type grows exponentially with the number of tetrahedra they are made of. We propose a model of 3D gravity interacting with scalar fermions, some restriction of which gives the 2-dimensional self-avoiding-loop-gas matrix model. We propose a qualitative picture of the phase structure of 3D simplicial gravity compatible with the numerical experiments and available analytical results.

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