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)

TL;DR

This paper establishes a new S-matrix formula in open string field theory by relating gauge invariant quantities to Feynman diagrams, providing a proof that certain Feynman rules reproduce on-shell amplitudes without traditional Feynman rule calculations.

Contribution

It derives recurrence relations linking gauge invariant quantities to Feynman diagrams and proves their equivalence to the S-matrix at tree level, validating new Feynman rules for on-shell amplitudes.

Findings

Gauge invariant quantity equals the tree-level S-matrix.

New Feynman rules reproduce on-shell disc amplitudes.

Recurrence relations connect gauge invariants with Feynman diagrams.

Abstract

We study relation between the gauge invariant quantity obtained in [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 in [arXiv:2003.05021 [hep-th]] reproduces the onshell disc amplitudes correctly by using the same combinatorial identities.