Ghost Sector of Vacuum String Field Theory and the Projection Equation

Details Ghost Sector of Vacuum String Field Theory and the Projection Equation Ghost Sector of Vacuum String Field Theory and the Projection Equation

2002-04-20

arxiv.org/abs/hep-th/0204172v2

JHEP 0206 (2002) 002

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, no figures. Typos corrected, published version

Scientific paper

10.1088/1126-6708/2002/06/002

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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