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Ghost Sector of Vacuum String Field Theory and the Projection Equation

Robertus Potting·Joris Raeymaekers
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Abstract

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.

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Robertus Potting, Joris Raeymaekers. 2002-07-17. Ghost Sector of Vacuum String Field Theory and the Projection Equation. https://doi.org/10.1088/1126-6708%2F2002%2F06%2F002

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