Ghost Structure and Closed Strings in Vacuum String Field Theory

TL;DR

This paper advances vacuum string field theory by defining a ghost kinetic term, enabling analytic solutions like projectors, and connecting open-string gauge invariants to closed string amplitudes.

Contribution

It introduces a canonical ghost kinetic term, simplifies the ghost sector analysis, and constructs gauge-invariant operators linked to closed string states.

Findings

Identification of new projectors, including butterfly surface states.

Analytic expressions for these projectors.

A framework connecting open-string gauge invariants to closed string amplitudes.

Abstract

We complete the construction of vacuum string field theory by proposing a canonical choice of ghost kinetic term -- a local insertion of the ghost field at the string midpoint with an infinite normalization. This choice, supported by level expansion studies in the Siegel gauge, allows a simple analytic treatment of the ghost sector of the string field equations. As a result, solutions are just projectors, such as the sliver, of an auxiliary CFT built by combining the matter part with a twisted version of the ghost conformal theory. Level expansion experiments lead to surprising new projectors -- butterfly surface states, whose analytical expressions are obtained. With the help of a suitable open-closed string vertex we define open-string gauge invariant operators parametrized by on-shell closed string states. We use regulated vacuum string field theory to sketch how pure closed string amplitudes on surfaces without boundaries arise as correlators of such gauge invariant operators.