Exact Results on Equations of Motion in Vacuum String Field Theory

TL;DR

This paper establishes algebraic relations for solutions in vacuum string field theory, generalizes half-string projectors, and embeds solutions into matrix equations, advancing the understanding of string field configurations.

Contribution

It introduces a generalized framework for half-string projectors and demonstrates embedding translationally invariant solutions into matrix equations, providing new insights into string field solutions.

Findings

Algebraic relations for solutions are proven.

Half-string projectors can be generalized beyond the sliver solution.

Translationally invariant solutions can be embedded into matrix equations.

Abstract

We prove some algebraic relations on the translationally invariant solutions and the lump solutions in vacuum string field theory. We show that up to the subtlety at the midpoint the definition of the half-string projectors of the known sliver solution can be generalized to other solutions. We also find that we can embed the translationally invariant solution into the matrix equation of motion with the zero mode.