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Schnabl recently found an analytic expression for the string field tachyoncondensate using a gauge condition adapted to the conformal frame of the sliverprojector. We propose that this construction is more general. The sliver is anexample of a special projector, a projector such that the Virasoro operator\L_0 and its BPZ adjoint \L*_0 obey the algebra [\L_0, \L*_0] = s (\L_0 +\L*_0), with s a positive real constant. All special projectors provide abeliansubalgebras of string fields, closed under both the *-product and the action of\L_0. This structure guarantees exact solvability of a ghost number zero stringfield equation. We recast this infinite recursive set of equations as anordinary differential equation that is easily solved. The classification ofspecial projectors is reduced to a version of the Riemann-Hilbert problem, withpiecewise constant data on the boundary of a disk.Comment: 64 pages, 6 figure

Solving open string field theory with special projectors