New approach to vacuum string field theory

We discuss the possibility of applying a purely ghost kinetic operator in open string field theory from the perspective of a modern analytic method based on the $KBc$ subalgebra. A purely ghost kinetic operator is obtained as a result of gauge fixing string field theory around the identity-based tachyon vacuum solution. We show that the obtained kinetic operator is not equivalent to the midpoint insertion of a conformal ghost, to which an extensive literature is devoted. We also show that the equation of motion does not admit nontrivial solutions.