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On-shell Recursion in String Theory

Rutger H. Boels, Daniele Marmiroli, Niels A. Obers

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.

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.

Paper Structure

This paper contains 26 sections, 184 equations, 1 figure, 5 tables.

Table of Contents

  1. Introduction
  2. Recursion relations for the disc: adjacent shifts
  3. Lightning review of on-shell recursion
  4. Veneziano revisited
  5. Adjacent shifts for all multiplicities
  6. Tachyon amplitudes in the bosonic string
  7. Gluon amplitudes in the bosonic string
  8. Gluon amplitudes in the superstring
  9. All open string tree amplitudes in a flat background
  10. Recursion relations for the disc: non-adjacent shifts
  11. Veneziano re-revisited
  12. Amplitude monodromy relations from the CFT
  13. Non-adjacent shifts from monodromy relations
  14. OPE derivation of adjacent shifts
  15. Shifting tachyons
  16. ...and 11 more sections

Figures (1)

  • Figure 1: Choice of contour on the interior of the disc.