Singular gauge transformations in string field theory

TL;DR

The paper demonstrates that all solutions in string field theory around the tachyon vacuum are gauge transformations of it, which are singular when non-trivial solutions are considered, highlighting the role of projectors in the star-algebra.

Contribution

It introduces a formalism showing all solutions are gauge transformations of the tachyon vacuum, emphasizing the significance of singular gauge transformations and projectors.

Findings

Solutions are gauge transformations of the tachyon vacuum.

Non-trivial solutions require singular gauge transformations.

Singular transformations relate to projectors in the star-algebra.

Abstract

We show that the existence of a tachyon vacuum puts tight restrictions on the form of solutions to the equations of motion of string field theory. In particular, we demonstrate that every solution can be written as a - formal - gauge transformation of the tachyon vacuum. In order for a solution to be non-trivial, this gauge transformation must be singular and we argue that this will happen when the gauge transformation annihilates a projector of the star-algebra. We comment on possible applications of the formalism to finding new solutions.