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

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

2000-07-17

arxiv.org/abs/math-ph/0007024v1

Physics

Mathematical Physics

32 pages

Scientific paper

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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