Constraints on a class of classical solutions in open string field theory

We calculate boundary states for general string fields in the KBc subalgebra under some regularity conditions based on the construction by Kiermaier, Okawa, and Zwiebach. The resulting boundary states are always proportional to that for the perturbative vacuum |B〉. In this framework, the equation of motion implies that boundary states are independent of the auxiliary parameter s associated with the length of the boundary. By requiring the s-independence, we show that the boundary states for classical solutions in our class are restricted to ±|B〉 and 0. In particular, there exist no string fields which reproduce boundary states for multiple D-brane backgrounds. While we know that the boundary states |B〉 and 0 are reproduced by solutions for the perturbative vacuum and the tachyon vacuum, respectively, no solutions reproducing −|B〉 have been constructed. In this paper we also propose a candidate for such a solution, which may describe the ghost D-brane.