Generating string field theory solutions with matter operators from $KBc$ algebra

TL;DR

This paper explores how the $KBc$ algebra can be extended with matter operators to generate various classical solutions in open string field theory, unifying different solutions within a common framework.

Contribution

It introduces operator sets satisfying the $KBc$ algebra that include matter operators, enabling the reproduction of known solutions like KOS and Erler-Maccaferri solutions.

Findings

Reproduced KOS and Erler-Maccaferri solutions using extended $KBc$ algebra.

Provided operator sets satisfying the $KBc$ algebra with matter operators.

Unified description of classical solutions in string field theory.

Abstract

The $KBc$ algebra is a subalgebra that has been used to construct classical solutions in Witten's open string field theory, such as the tachyon vacuum solution. The main purpose of this paper is to give various operator sets that satisfy the $KBc$ algebra. In addition, since those sets can contain matter operators arbitrarily, we can reproduce the KOS and the Erler-Maccaferri solutions. Starting with a single D-brane solution on the tachyon vacuum, we replace the original $KBc$ in it with an appropriate set to generate each of the above solutions. Thus, it is expected that the $KBc$ algebra, combined with the single D-brane solution, leads to a more unified description of classical solutions.