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The modular geometry of Random Regge Triangulations

M. Carfora·C. Dappiaggi·A. Marzuoli
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Abstract

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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M. Carfora, C. Dappiaggi, A. Marzuoli. 2002-09-27. The modular geometry of Random Regge Triangulations. https://doi.org/10.1088/0264-9381%2F19%2F20%2F312

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