The geometry of dynamical triangulations

Details The geometry of dynamical triangulations The geometry of dynamical triangulations

1996-12-06

arxiv.org/abs/hep-th/9612069v1

Lect.NotesPhys.50:197,1997

Physics

High Energy Physics

High Energy Physics - Theory

166 pages, Revtex (latex) file

Scientific paper

We discuss the geometry of dynamical triangulations associated with 3-dimensional and 4-dimensional simplicial quantum gravity. We provide analytical expressions for the canonical partition function in both cases, and study its large volume behavior. In the space of the coupling constants of the theory, we characterize the infinite volume line and the associated critical points. The results of this analysis are found to be in excellent agreement with the MonteCarlo simulations of simplicial quantum gravity. In particular, we provide an analytical proof that simply-connected dynamically triangulated 4-manifolds undergo a higher order phase transition at a value of the inverse gravitational coupling given by 1.387, and that the nature of this transition can be concealed by a bystable behavior. A similar analysis in the 3-dimensional case characterizes a value of the critical coupling (3.845) at which hysteresis effects are present.

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