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

TL;DR

This paper explores the deep geometric connections between Regge surfaces, dynamical triangulations, and moduli space intersection theory, revealing a duality and providing explicit measures related to the geometry of Riemann surfaces.

Contribution

It establishes a novel link between Regge measures, dynamical triangulations, and intersection theory on moduli spaces, suggesting a form of topological S-duality.

Findings

Regge measures relate to volumes of moduli space strata

Explicit connection between triangulation counts and intersection theory

Evidence for topological S-duality between Regge calculus and DT theory

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.