Feynman rules for string field theories with discrete target space

TL;DR

This paper derives a minimal set of Feynman rules for calculating loop amplitudes in closed string models with target spaces represented by simply laced Dynkin diagrams, providing explicit formulas for certain amplitudes.

Contribution

It introduces a simplified framework of Feynman rules for string field theories with discrete target spaces, including explicit expressions for complex amplitudes.

Findings

Derived Feynman rules for loop amplitudes in discrete target space models

Explicit formulas for genus-one tadpole and genus-zero four-loop amplitude

Demonstrated factorization of vertices into matter fusion and intersection numbers

Abstract

We derive a minimal set of Feynman rules for the loop amplitudes in unitary models of closed strings, whose target space is a simply laced (extended) Dynkin diagram. The string field Feynman graphs are composed of propagators, vertices (including tadpoles) of all topologies, and leg factors for the macroscopic loops. A vertex of given topology factorizes into a fusion coefficient for the matter fields and an intersection number associated with the corresponding punctured surface. As illustration we obtain explicit expressions for the genus-one tadpole and the genus-zero four-loop amplitude.