Triangulated Surfaces in Twistor Space: A Kinematical Set up for Open/Closed String Duality

TL;DR

This paper presents a novel geometric framework using hyperbolic space and twistorial fields to explore open/closed string duality, linking Regge triangulations with intersection theory and Chern-Simons theory.

Contribution

It introduces a simplicial model connecting open and closed string theories via twistorial triangulations and maps twistorial N-point functions into intersection theory.

Findings

Twistorial N-point functions map into Witten-Kontsevich intersection theory.

The model connects hyperbolic geometry with Chern-Simons theory.

Provides a geometric setting for open/closed string duality.

Abstract

We exploit the properties of the three-dimensional hyperbolic space to discuss a simplicial setting for open/closed string duality based on (random) Regge triangulations decorated with null twistorial fields. We explicitly show that the twistorial N-points function, describing Dirichlet correlations over the moduli space of open N-bordered genus g surfaces, is naturally mapped into the Witten-Kontsevich intersection theory over the moduli space of N-pointed closed Riemann surfaces of the same genus. We also discuss various aspects of the geometrical setting which connects this model to PSL(2,C) Chern-Simons theory.