Associativity Anomaly in String Field Theory

TL;DR

This paper investigates the associativity anomaly in open string field theory, linking it to infinite matrices and midpoint issues, and proposes a finite mode cutoff method to ensure consistent associativity.

Contribution

It identifies the origin of the anomaly related to infinite matrices and midpoint issues, and introduces a finite mode cutoff approach for consistent calculations.

Findings

The anomaly is connected to properties of infinite size matrices.

A subspace related to closed string configurations causes the anomaly.

A finite mode cutoff method guarantees associativity during computations.

Abstract

We give a detailed study of the associativity anomaly in open string field theory from the viewpoint of the split string and Moyal formalisms. The origin of the anomaly is reduced to the properties of the special infinite size matrices which relate the conventional open string to the split string variables, and is intimately related to midpoint issues. We discuss two steps to cope with the anomaly. We identify the field subspace that causes the anomaly which is related to the existence of closed string configurations, and indicate a decomposition of open/closed string sectors. We then propose a consistent cut off method with a finite number of string modes that guarantees associativity at every step of any computation.