Connecting Solutions in Open String Field Theory with Singular Gauge Transformations

TL;DR

This paper explores how classical solutions in open string field theory can be connected via singular gauge transformations, revealing a categorical structure and conditions for generating new solutions.

Contribution

It demonstrates that solutions can be related by gauge transformations without inverses and introduces a framework linking these transformations to star algebra projectors.

Findings

Gauge transformations without inverses relate classical solutions.

Conditions for generating new solutions via gauge parameters.

Singular gauge transformations induce a categorical structure in solution space.

Abstract

We show that any pair of classical solutions of open string field theory can be related by a formal gauge transformation defined by a gauge parameter $U$ without an inverse. We investigate how this observation can be used to construct new solutions. We find that a choice of gauge parameter consistently generates a new solution only if the BRST charge maps the image of $U$ into itself. When this occurs, we argue that $U$ naturally defines a star algebra projector which describes a surface of string connecting the boundary conformal field theories of the classical solutions related by $U$. We also note that singular gauge transformations give the solution space of open string field theory the structure of a category, and we comment on the physical interpretation of this observation.