Singularities in K-space and multi-brane solutions in cubic string field theory

Abstract

In a previous paper [arXiv:1111.2389], we studied the multi-brane solutions in cubic string field theory by focusing on the topological nature of the “winding number” $\mathcal{N}$ which counts the number of branes. We found that $\mathcal{N}$ can be non-trivial owing to the singularity from the zero-eigenvalue of K of the KBc algebra, and that solutions carrying integer $\mathcal{N}$ and satisfying the EOM in the strong sense is possible only for $\mathcal{N}$ = 0, ±1. In this paper, we extend the construction of multi-brane solutions to $\left| \mathcal{N} \right|$ ≥ 2. The solutions with N =±2ismadepossiblebythefactthatthecorrelatorisinvariantunderatransformation exchanging K with 1/K and hence K = ∞ eigenvalue plays the same role as K = 0. We further propose a method of constructing solutions with $\left| \mathcal{N} \right|$ ≥ 3 by expressing the eigenvalue space of K as a sum of intervals where the construction for $\left| \mathcal{N} \right|$ ≤ 2 is applicable.