On different actions for the vacuum of bosonic string field theory

TL;DR

This paper explores a family of kinetic operators in bosonic string field theory around the closed string vacuum, clarifying their gauge relations and connecting them to known propagators.

Contribution

It introduces a generalized class of kinetic operators based on Takahashi and Tanimoto's solutions, extending vacuum string field theory and analyzing their gauge properties.

Findings

Operators are less singular than pure ghost operators.

Different representations are related by gauge transformations.

The Siegel gauge recovers a known closed string propagator.

Abstract

We study a family of kinetic operators in string field theory describing the theory around the closed string vacuum. Those operators are based on the analytical classical solutions of Takahashi and Tanimoto and are analogous to the pure ghost action usually referred to as "vacuum string field theory," but are much more general, and less singular than the pure ghost operator. The closed string vacuum is related to the D-brane vacuum by large, singular, gauge transformations or field redefinition, and all those different representations are related to each other by small gauge transformations. We try to clarify the nature of this singular gauge transformation. We also show that by choosing the Siegel gauge one recovers the propagator proposed in hep-th/0207266 that generates closed string surfaces.