Exploring Vacuum Structure around Identity-Based Solutions

TL;DR

This paper investigates the vacuum structure in bosonic open string field theory around an identity-based solution, revealing different vacuum states depending on a parameter, using level truncation approximation.

Contribution

It demonstrates that the identity-based solution behaves as a pure gauge for a>-1/2 and as a tachyon vacuum at a=-1/2, providing new insights into string field theory vacua.

Findings

Tachyon vacuum exists for a>-1/2

Unstable vacuum at a=-1/2 corresponds to perturbative vacuum

Level truncation up to level 20 supports these results

Abstract

We explore the vacuum structure in bosonic open string field theory expanded around an identity-based solution parameterized by $a(>=-1/2)$. Analyzing the expanded theory using level truncation approximation up to level 20, we find that the theory has the tachyon vacuum solution for $a>-1/2$. We also find that, at $a=-1/2$, there exists an unstable vacuum solution in the expanded theory and the solution is expected to be the perturbative open string vacuum. These results reasonably support the expectation that the identity-based solution is a trivial pure gauge configuration for $a>-1/2$, but it can be regarded as the tachyon vacuum solution at $a=-1/2$.