On-shell Recursion in String Theory

TL;DR

This paper proves that open and closed string theory amplitudes obey BCFW on-shell recursion relations, extending the technique from field theory to string theory and exploring its implications and generalizations.

Contribution

It establishes BCFW recursion relations for open and closed string amplitudes, providing a novel CFT derivation and connecting string dualities.

Findings

Open string amplitudes obey BCFW recursion relations.

Field theory limit of string amplitudes is smooth.

Recursion relations extend to backgrounds like constant B-field.

Abstract

We prove that all open string theory disc amplitudes in a flat background obey Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion relations, up to a possible reality condition on a kinematic invariant. Arguments that the same holds for tree level closed string amplitudes are given as well. Non-adjacent BCFW-shifts are related to adjacent shifts through monodromy relations for which we provide a novel CFT based derivation. All possible recursion relations are related by old-fashioned string duality. The field theory limit of the analysis for amplitudes involving gluons is explicitly shown to be smooth for both the bosonic string as well as the superstring. In addition to a proof a less rigorous but more powerful argument based on the underlying CFT is presented which suggests that the technique may extend to a much more general setting in string theory. This is illustrated by a discussion of the open string in a constant B-field background and the closed string on the level of the sphere.