  We study the ghost sector of vacuum string field theory where the BRST
operator Q is given by the midpoint insertion proposed by Gaiotto, Rastelli,
Sen and Zwiebach. We introduce a convenient basis of half-string modes in terms
of which Q takes a particularly simple form. We show that there exists a field
redefinition which reduces the ghost sector field equation to a pure projection
equation for string fields satisfying the constraint that the ghost number is
equally divided over the left- and right halves of the string. When this
constraint is imposed, vacuum string field theory can be reformulated as a
$U(\infty)$ cubic matrix model. Ghost sector solutions can be constructed from
projection operators on half-string Hilbert space just as in the matter sector.
We construct the ghost sector equivalent of various well-known matter sector
projectors such as the sliver, butterfly and nothing states.
