Analytic Study of Nonperturbative Solutions in Open String Field Theory

TL;DR

This paper develops an analytic approach to find nonperturbative solutions in open string field theory using the Moyal star formulation, revealing a class of solutions including a stable butterfly state.

Contribution

It introduces a novel analytic framework based on the Moyal star formulation to solve the nonlinear equations of open string field theory nonperturbatively.

Findings

Exact solutions classified by projection operators.

Identification of a unique stable solution, the butterfly state.

Perturbative inclusion of midpoint corrections to exact solutions.

Abstract

We propose an analytic framework to study the nonperturbative solutions of Witten's open string field theory. The method is based on the Moyal star formulation where the kinetic term can be split into two parts. The first one describes the spectrum of two identical half strings which are independent from each other. The second one, which we call midpoint correction, shifts the half string spectrum to that of the standard open string. We show that the nonlinear equation of motion of string field theory is exactly solvable at zeroth order in the midpoint correction. An infinite number of solutions are classified in terms of projection operators. Among them, there exists only one stable solution which is identical to the standard butterfly state. We include the effect of the midpoint correction around each exact zeroth order solution as a perturbation expansion which can be formally summed to the complete exact solution.