Proof of vanishing cohomology at the tachyon vacuum

TL;DR

This paper proves Sen's third conjecture in open bosonic string field theory, showing no perturbative excitations at the tachyon vacuum by constructing an explicit analytic state related to the BRST operator.

Contribution

It provides an analytic expression for a special state that confirms the absence of on-shell excitations at the tachyon vacuum, advancing understanding of string field theory.

Findings

Confirmed no perturbative excitations at the tachyon vacuum

Constructed an explicit analytic state related to the BRST operator

Validated numerical findings with a simple analytic expression

Abstract

We prove Sen's third conjecture that there are no on-shell perturbative excitations of the tachyon vacuum in open bosonic string field theory. The proof relies on the existence of a special state A, which, when acted on by the BRST operator at the tachyon vacuum, gives the identity. While this state was found numerically in Feynman-Siegel gauge, here we give a simple analytic expression.