The Phantom Term in Open String Field Theory

TL;DR

This paper introduces the concept of the phantom term in open string field theory, showing how it relates two classical solutions via a singular gauge transformation and its applications in computing gauge invariant observables.

Contribution

It formalizes the phantom term as a singular, projector-like state connecting solutions, advancing understanding of background shifts in string field theory.

Findings

The phantom term can be explicitly constructed from classical solutions.

It provides a new method to compute gauge invariant observables.

The approach clarifies the role of singular gauge transformations in string theory.

Abstract

We show that given any two classical solutions in open string field theory and a singular gauge transformation relating them, it is possible to write the second solution as a gauge transformation of the first plus a singular, projector-like state which describes the shift in the open string background between the two solutions. This is the "phantom term." We give some applications in the computation of gauge invariant observables.