String Amplitudes from Moyal String Field Theory

TL;DR

This paper develops analytic methods for computing string field theory Feynman graphs using Moyal star formulation, applicable to both perturbative and nonperturbative states, and clarifies the structure of certain string theories.

Contribution

It introduces efficient computational techniques based on monoid algebra and Fourier space Feynman rules within Moyal string field theory, enhancing analytic calculations.

Findings

Methods apply to perturbative and nonperturbative states

Provides clarification on midpoint structures in string theories

Formulates ghost sector using Moyal products with fermionic ghosts

Abstract

We illustrate a basic framework for analytic computations of Feynman graphs using the Moyal star formulation of string field theory. We present efficient methods of computation based on (a) the monoid algebra in noncommutative space and (b) the conventional Feynman rules in Fourier space. The methods apply equally well to perturbative string states or nonperturbative string states involving D-branes. The ghost sector is formulated using Moyal products with fermionic (b,c) ghosts. We also provide a short account on how the purely cubic theory and/or VSFT proposals may receive some clarification of their midpoint structures in our regularized framework.