Analytical construction of a nonperturbative vacuum for the open bosonic string

TL;DR

The paper presents an analytical construction of a nonperturbative, Lorentz-invariant vacuum ${\cal N}$ for open bosonic string field theory by recasting the cubic vertex in a momentum representation and exploiting squeezed-state techniques. A central ingredient is a squeezed string field ${\cal S}$ satisfying ${\cal S}\star{\cal S}=c_0{\cal S}$, obtained via a Bogoliubov transformation to a basis where ${\cal S}$ is the vacuum; the nonperturbative vacuum ${\cal N}$ is then built as a twisted product around ${\cal S}$, with a systematic expansion in the width $S$ that yields a normalizable state whose low-lying excitations are heavy and whose energy matches a large fraction of the D25-brane tension. The construction yields explicit closed-form matrices for $S$ and $\tilde{S}$ in terms of the vertex data, demonstrates consistency with level-truncation results, and suggests a broad applicability to lump solutions, D-branes of various dimensionalities, and potentially closed-string sectors. The work provides a concrete analytical handle on tachyon condensation and reinforces the interpretation of the Lorentz-invariant nonperturbative vacuum as the endpoint of brane decay in open bosonic string theory.

Abstract

Using analytical methods, a nonpertubative vacuum is constructed recursively in the field theory for the open bosonic string. Evidence suggests it corresponds to the Lorentz-invariant endpoint of tachyon condensation on a D25-brane. The corresponding string field is a twisted squeezed state.