Comments on new multiple-brane solutions based on Hata-Kojita duality in open string field theory

Recently, Hata and Kojita proposed a new energy formula for a class of solutions in Witten's open string field theory based on a novel symmetry of correlation functions they found. Their energy formula can be regarded as a generalization of the conventional energy formula by Murata and Schnabl. Following their proposal, we investigate their new ansatz for the classical solution representing double D-branes. We present a regularized definition of this solution and show that the solution satisfies the equation of motion when it is contracted with the solution itself and when it is contracted with any states in the Fock space. However, the Ellwood invariant and the boundary state of the solution are the same as those for the perturbative vacuum. This result disagrees with an expectation from the Ellwood conjecture.
31 pages; v5: the formula (1.7) and (3.5) corrected; a proof of the formula (3.2) added; a new paragraph added at the end of appendix C; typos corrected