On the spectrum around numerical solutions in Siegel gauge in open string field theory

In bosonic open string field theory, the spectrum around the numerical tachyon vacuum solution in Siegel gauge was investigated by Giusto and Imbimbo. Using their numerical method, we study the mass spectrum around two other solutions, which are ``double brane'' and ``single brane" solutions in Siegel gauge constructed by the level truncation approximation. The ``double brane'' solution was constructed by Kudrna and Schnabl and its energy might correspond to a double brane. On the other hand, the ``single brane'' solution was constructed by Takahashi and the author in the theory around the identity-based solution for the tachyon vacuum and its energy corresponds to the perturbative vacuum, namely, a single brane. From the eigenvalues of the matrix for the kinetic term in Siegel gauge, we find a tachyon state and a massless vector state in the ghost number one sector around the ``single brane'' solution, which is consistent with the perturbative vacuum, although the mass spectrum around the ``double brane'' solution is obscure up to the truncation level ten and within scalar and vector states.