Proof of new S-matrix formula from classical solutions in open string field theory: Or, deriving on-shell open string field amplitudes without using Feynman rules, Part II

Abstract

Abstract We study the relation between the gauge-invariant quantity obtained by T. Masuda and H. Matsunaga (arXiv:1908.09784) and the Feynman diagrams in the dressed $\mathcal {B}_0$ gauge in the open cubic string field theory. We derive a set of recurrence relations that hold among the terms of this gauge-invariant quantity. By using these relations, we prove that this gauge-invariant quantity equals the S-matrix at the tree level. We also present a proof that a set of new Feynman rules proposed by T. Masuda and H. Matsunaga (arXiv:2003.05021) reproduces the on-shell disk amplitudes correctly by using the same combinatorial identities.