Ghost Kinetic Operator of Vacuum String Field Theory

TL;DR

This paper analytically proves that the ghost kinetic operator in vacuum string field theory is equivalent to the midpoint ghost insertion, providing insights into the structure of the theory and related determinants.

Contribution

It demonstrates analytically the equivalence of the ghost kinetic operator to the midpoint insertion using eigenvalues and eigenvectors of Neumann matrices.

Findings

Ghost kinetic operator equals midpoint ghost insertion

Analytic proof based on eigenvalues and eigenvectors

Comments on determinants in sliver state norm

Abstract

Using the data of eigenvalues and eigenvectors of Neumann matrices in the 3-string vertex, we prove analytically that the ghost kinetic operator of vacuum string field theory obtained by Hata and Kawano is equal to the ghost operator inserted at the open string midpoint. We also comment on the values of determinants appearing in the norm of sliver state.