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Moduli space intersection duality between Regge surfaces and 2D dynamical triangulations

Mauro Carfora·Annalisa Marzuoli·Paolo Villani
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Abstract

Deformation theory for 2-dimensional dynamical triangulations with N vertices is discussed by exploiting the geometry of the moduli space of Euclidean polygons. Such an analysis provides an explicit connection among Regge surfaces, dynamical triangulations and the Witten-Kontsevich model. We show that a natural set of Regge measures and a triangulation counting of relevance for dynamical triangulations are directly connected with intersection theory over the compactified moduli space of genus g Riemann surfaces with N punctures.The Regge measures in question provide volumes of the open strata in moduli space. It is also argued that the arguments presented here offer evidence of a form of topological S-duality between Regge calculus and DT theory.

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Mauro Carfora, Annalisa Marzuoli, Paolo Villani. 2000-07-17. Moduli space intersection duality between Regge surfaces and 2D dynamical triangulations. https://arxiv.org/abs/math-ph/0007024

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