BV analysis of tachyon fluctuation around multi-brane solutions in cubic string field theory

We study whether the tachyon mode exists as a physical fluctuation on the 2-brane solution and on the tachyon vacuum solution in cubic open string field theory. our analysis is based on the batalin-vilkovisky formalism. we first construct a set of six string states which corresponds to the set of fields and anti-fields containing the tachyon field. whether the tachyon field can exist as a physical fluctuation is determined by the 6 × 6 matrix defining the anti-bracket in the present sector. if the matrix is degenerate/non-degenerate, the tachyon field is physical/unphysical. calculations for the pure-gauge type solutions in the framework of the kbc algebra and using the k ε -regularization lead to the expected results. namely, the matrix for the anti-bracket is degenerate/non-degenerate in the case of the 2-brane/tachyon-vacuum solution. our analysis is not complete, in particular, in that we have not identified the four-fold degeneracy of tachyon fluctuation on the 2-brane solution, and moreover that the present six states do not satisfy the hermiticity condition.