Computing in String Field Theory Using the Moyal Star Product

TL;DR

This paper introduces a simplified, precise formulation of open bosonic string field theory using the Moyal star product, enabling easier computation of string interactions and configurations, and explores the implications of an associativity anomaly in VSFT.

Contribution

It provides a new Moyal star product-based formulation of string field theory, simplifying calculations and identifying key algebraic structures and anomalies.

Findings

Moyal star product suffices for defining string field theory

Simplified computation of string vertices and configurations

Identification of an associativity anomaly in VSFT

Abstract

Using the Moyal star product, we define open bosonic string field theory carefully, with a cutoff, for any number of string oscillators and any oscillator frequencies. Through detailed computations, such as Neumann coefficients for all string vertices, we show that the Moyal star product is all that is needed to give a precise definition of string field theory. The formulation of the theory as well as the computation techniques are considerably simpler in the Moyal formulation. After identifying a monoid algebra as a fundamental mathematical structure in string field theory, we use it as a tool to compute with ease the field configurations for wedge, sliver, and generalized projectors, as well as all the string interaction vertices for perturbative as well as monoid-type nonperturbative states. Finally, in the context of VSFT we analyze the small fluctuations around any D-brane vacuum. We show quite generally that to obtain nontrivial mass and coupling, as well as a closed strings, there must be an associativity anomaly. We identify the detailed source of the anomaly, but leave its study for future work.