VSFT revisited

TL;DR

This paper revisits the validity of purely ghost kinetic operators in open string field theory, demonstrating their differences from known operators and showing the absence of nontrivial solutions in the equations of motion.

Contribution

It provides a modern analytic perspective on ghost kinetic operators, clarifying their properties and limitations in the context of the $K B c$ subalgebra.

Findings

Purely ghost kinetic operator differs from midpoint ghost insertion.

Equation of motion admits no nontrivial solutions.

Validates the gauge fixing approach around the tachyon vacuum.

Abstract

We argue validity of purely ghost kinetic operator in open string field theory from the perspective of the modern analytic method based on the $K B c$ subalgebra. A purely ghost kinetic operator is obtained as a result of gauge fixing string field theory around the identity based tachyon vacuum solution. It is shown that the obtained kinetic operator is not equivalent to the midpoint insertion of the conformal ghost which is extensively studied in literature. We also find that the equation of motion does not allow any nontrivial solutions.