Pinching parameters for open (super) strings

TL;DR

The paper introduces a new parametrization of (super) Schottky space using sewing of three-punctured discs, which simplifies the analysis of string propagators and their connection to Feynman graphs in the IR limit.

Contribution

It provides a novel parametrization method for (super) Schottky space based on cubic ribbon graphs, facilitating the study of IR behavior and the connection to Feynman diagrams.

Findings

Convergence of worldsheet Green's functions to Symanzik polynomials as $\,\alpha'\to 0$

Simplified form of the (super) string measure in the new parameters

Mapping between different sets of pinching parameters via ribbon graphs

Abstract

We present an approach to the parametrization of (super) Schottky space obtained by sewing together three-punctured discs with strips. Different cubic ribbon graphs classify distinct sets of pinching parameters; we show how they are mapped onto each other. The parametrization is particularly well-suited to describing the region within (super) moduli space where open bosonic or Neveu-Schwarz string propagators become very long and thin, which dominates the IR behaviour of string theories. We show how worldsheet objects such as the Green's function converge to graph theoretic objects such as the Symanzik polynomials in the $\alpha ' \to 0$ limit, allowing us to see how string theory reproduces the sum over Feynman graphs. The (super) string measure takes on a simple and elegant form when expressed in terms of these parameters.