Comments on lump solutions in SFT

TL;DR

This paper critically examines a scheme for constructing analytic lump solutions in open string field theory, emphasizing the importance of consistent conformal field theory frameworks and proposing improvements to older solution proposals.

Contribution

It clarifies the conditions for background independence in lump solutions and introduces a distinction between regular and singular gauge transformations in string field theory.

Findings

The scheme requires implementation within the same 2D conformal field theory.

Improved the understanding of analytic lump solutions in SFT.

Highlighted the need for a topology in the space of string fields.

Abstract

We analyze a recently proposed scheme to construct analytic lump solutions in open SFT. We argue that in order for the scheme to be operative and guarantee background independence it must be implemented in the same 2D conformal field theory in which SFT is formulated. We outline and discuss two different possible approaches. Next we reconsider an older proposal for analytic lump solutions and implement a few improvements. In the course of the analysis we formulate a distinction between regular and singular gauge transformations and advocate the necessity of defining a topology in the space of string fields.