Fluctuations around the Tachyon Vacuum in Open String Field Theory

TL;DR

This paper numerically analyzes quadratic fluctuations around the tachyon vacuum in open string field theory, demonstrating the stability and minimal energy nature of Schnabl's vacuum solution.

Contribution

It introduces a numerical framework for studying fluctuations around the tachyon vacuum using a truncated basis, confirming the stability of Schnabl's solution.

Findings

Schnabl's vacuum solution is well-behaved numerically.

The orthogonal basis for the new BRST operator is constructed.

Results support that the vacuum is a minimum energy state.

Abstract

We consider quadratic fluctuations around the tachyon vacuum numerically in open string field theory. We work on a space ${\cal H}_N^{{\rm vac}}$ spanned by basis string states used in the Schnabl's vacuum solution. We show that the truncated form of the Schnabl's vacuum solution on ${\cal H}_N^{{\rm vac}}$ is well-behaved in numerical work. The orthogonal basis for the new BRST operator $\tilde Q$ on ${\cal H}_N^{{\rm vac}}$ and the quadratic forms of potentials for independent fields around the vacuum are obtained. Our numerical results support that the Schnabl's vacuum solution represents the minimum energy solution for arbitrary fluctuations also in open string field theory.