Level truncation and the quartic tachyon coupling

TL;DR

This paper investigates the convergence of level truncation in bosonic open string field theory by calculating the quartic tachyon coupling up to level 28 and extrapolating to infinite level, providing precise numerical results.

Contribution

It presents a detailed analysis of the convergence behavior of level truncation and introduces a self-consistent method to determine the coupling and correction exponent.

Findings

Exact quartic tachyon coupling: -1.7422006(9)

Leading correction exponent: approximately 1

Convergence behavior characterized by BST algorithm

Abstract

We discuss the convergence of level truncation in bosonic open string field theory. As a test case we consider the calculation of the quartic tachyon coupling $\gamma_4$. We determine the exact contribution from states up to level L=28 and discuss the $L\to\infty$ extrapolation by means of the BST algorithm. We determine in a self-consistent way both the coupling and the exponent $\omega$ of the leading correction to $\gamma_4$ at finite $L$ that we assume to be $\sim 1/L^\omega$. The results are $\gamma_4 = -1.7422006(9)$ and $|\omega-1|\lesssim 10^{-4}$.}