MHV, CSW and BCFW: field theory structures in string theory amplitudes

TL;DR

This paper explores how field theory amplitude techniques like MHV, CSW, and BCFW can be applied to string theory, revealing new structures and recursion relations in open superstring amplitudes.

Contribution

It demonstrates the reduction of alpha'-corrections to polynomial calculations, derives a trivial CSW-like series from the Dirac-Born-Infeld action, and establishes BCFW recursion relations for open string amplitudes.

Findings

Alpha'-corrections reduce to polynomial determination.

CSW-like series only non-zero for helicity conserving amplitudes.

Open string four-point amplitudes obey BCFW recursion relations.

Abstract

Motivated by recent progress in calculating field theory amplitudes, we study applications of the basic ideas in these developments to the calculation of amplitudes in string theory. We consider in particular both non-Abelian and Abelian open superstring disk amplitudes in a flat space background, focusing mainly on the four-dimensional case. The basic field theory ideas under consideration split into three separate categories. In the first, we argue that the calculation of alpha'-corrections to MHV open string disk amplitudes reduces to the determination of certain classes of polynomials. This line of reasoning is then used to determine the alpha'^3-correction to the MHV amplitude for all multiplicities. A second line of attack concerns the existence of an analog of CSW rules derived from the Abelian Dirac-Born-Infeld action in four dimensions. We show explicitly that the CSW-like perturbation series of this action is surprisingly trivial: only helicity conserving amplitudes are non-zero. Last but not least, we initiate the study of BCFW on-shell recursion relations in string theory. These should appear very naturally as the UV properties of the string theory are excellent. We show that all open four-point string amplitudes in a flat background at the disk level obey BCFW recursion relations. Based on the naturalness of the proof and some explicit results for the five-point gluon amplitude, it is expected that this pattern persists for all higher point amplitudes and for the closed string.