Singularities in K-space and Multi-brane Solutions in Cubic String Field Theory

TL;DR

This paper extends the construction of multi-brane solutions in cubic string field theory to cases where the winding number N is greater than or equal to 2, by analyzing singularities in the K-space and utilizing symmetries.

Contribution

It introduces a method to construct multi-brane solutions with |N| extgreater= 2 by exploiting K-space symmetries and eigenvalue interval decomposition.

Findings

Solutions with N=±2 are constructed using K=∞ eigenvalue symmetry.

A new method for solutions with |N| extgreater= 3 is proposed based on eigenvalue space decomposition.

The topological winding number N is linked to singularities in the K-space eigenvalues.

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" N which counts the number of branes. We found that N can be non-trivial owing to the singularity from the zero-eigenvalue of K of the KBc algebra, and that solutions carrying integer N and satisfying the EOM in the strong sense is possible only for N=0,\pm 1. In this paper, we extend the construction of multi-brane solutions to |N|\ge 2. The solutions with N=\pm 2 is made possible by the fact that the correlator is invariant under a transformation exchanging K with 1/K and hence K=\infty eigenvalue plays the same role as K=0. We further propose a method of constructing solutions with |N|\ge 3 by expressing the eigenvalue space of K as a sum of intervals where the construction for |N|\le 2 is applicable.