On-shell Recursion in String Theory

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.

36 + 9 pages text, one figure, v3: added discussion on relation to old-fashioned factorization, typos corrected, published version

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Cited by in corpus (13)

• The Momentum Kernel of Gauge and Gravity Theories
• Black Hole Formation and Classicalization in Ultra-Planckian 2 -> N Scattering
• On the Tensionless Limit of String theory, Off - Shell Higher Spin Interaction Vertices and BCFW Recursion Relations
• A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
• On-shell constructibility of tree amplitudes in general field theories
• Recursion Relations for AdS/CFT Correlators
• On BCFW shifts of integrands and integrals
• On higher derivative corrections to Wess-Zumino and Tachyonic actions in type II super string theory
• Pomerons and BCFW recursion relations for strings on D-branes
• On tree amplitudes with gluons coupled to gravitons
• Three Point Tree Level Amplitude in Superstring Theory
• Disk level S-matrix elements at eikonal Regge limit
• Bonus scaling and BCFW in N=7 supergravity