The modular geometry of Random Regge Triangulations

Details The modular geometry of Random Regge Triangulations The modular geometry of Random Regge Triangulations

2002-06-26

arxiv.org/abs/gr-qc/0206077v2

Class.Quant.Grav. 19 (2002) 5195-5220

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

36 pages corrected typos, enhanced introduction

Scientific paper

10.1088/0264-9381/19/20/312

We show that the introduction of triangulations with variable connectivity and fluctuating egde-lengths (Random Regge Triangulations) allows for a relatively simple and direct analyisis of the modular properties of 2 dimensional simplicial quantum gravity. In particular, we discuss in detail an explicit bijection between the space of possible random Regge triangulations (of given genus g and with N vertices) and a suitable decorated version of the (compactified) moduli space of genus g Riemann surfaces with N punctures. Such an analysis allows us to associate a Weil-Petersson metric with the set of random Regge triangulations and prove that the corresponding volume provides the dynamical triangulation partition function for pure gravity.

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