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 stable and unstable vacua depending on a parameter, with numerical evidence supporting the interpretation of the solutions.

Contribution

It provides a detailed numerical analysis of the vacuum structure around an identity based solution using level truncation, clarifying the nature of the vacua for different parameter values.

Findings

Stable vacuum exists for a > -1/2.

Vacuum energy approaches tachyon vacuum values with higher truncation levels.

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

Abstract

We explore vacuum structure in bosonic open string field theory expanded around an identity based solution parameterized by $a$ (>= -1/2). Analyzing the expanded theory by using level truncation approximation up to level 14, we find that the theory has a stable vacuum solution for $a$>-1/2. The vacuum energy and the gauge invariant overlap numerically approach those of the tachyon vacuum solution with increasing truncation level. Also we find that, at $a$=-1/2, there exists an unstable vacuum solution in the expanded theory and it rapidly becomes the trivial zero configuration just above $a$=-1/2. The numerical behavior of the two gauge invariants suggests that the unstable solution corresponds to 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.