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

TL;DR

This paper investigates how recent field-theory amplitude techniques can illuminate string theory amplitudes. It develops a symmetry- and SUSY-driven framework to determine alpha' corrections to MHV open-string amplitudes, successfully deriving explicit all-mmultiplicity results up to alpha'^3 and organizing them via cyclically reducible polynomials. It also shows that the Abelian DBI action yields a surprisingly simple, helicity-conserving (partial CSW) perturbation theory, while initiating a BCFW-like on-shell recursion program for string amplitudes, providing explicit evidence that residues at infinity vanish for disk-level open-string amplitudes in several cases. Collectively, these results suggest a deeper field-theory–string-theory bridge where tree-level amplitudes may be constructed from a small set of on-shell building blocks, with promising connections to twistor techniques and possible extensions to non-Abelian and closed-string sectors.

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.

Figures (5)

• Figure 1: Conformal symmetry elucidates a certain kinematical limit with $k$ a non-negative integer. The sum runs over all string states at this particular mass level.
• Figure 2: Illustration of the two types of contribution to the $8$-point amplitude: non-local (left) and local (right).
• Figure 3: A graphical illustration of $5$-gluon amplitude recursion diagrams
• Figure 4: Illustration of the Schouten identity in 2 dimensions. Dots represent indices, brackets represent contraction of the indices by the epsilon tensor.
• Figure 5: Examples of 'good' (left) and 'bad' (right) terms in the direct, naive application of BCFW recursion relations for Abelian superstring amplitudes.

Theorems & Definitions (1)

• Definition