Universal Solutions in Open String Field Theory

An outstanding problem in open bosonic string field theory is the existence of nontrivial classical solutions in its universal sector. Such solutions independent of the underlying CFT would be relevant for any background, but aside of the celebrated tachyon vacuum, no well behaved solutions have been found so far. In this work we revisit the problem using the old fashioned level truncation technique, but armed with much more sophisticated techniques and greater computer power. In particular, using the homotopy continuation method we construct all solutions at level 6 (or 5) with twist symmetry imposed (or not), and improve the viable ones by Newton's method to levels 24-30. Surprisingly, a handful of solutions survive. One of them is tantalizingly close to the elusive double brane solution, although the fits to infinite level seem to invalidate this conclusion. A better behaved solution matches unexpectedly the properties of a ghost brane. This does not contradict anything, since the solution violates the reality condition of string field theory. Relaxing SU(1,1) singlet condition two more exotic solutions with the rough characteristics of half brane and ghost half brane are found. For the tachyon vacuum, by explicit numerical computations up to level 30, we confirm the Gaiotto and Rastelli's prediction about the turning point of the tachyon potential minimum as a function of the level.