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

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.