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

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 α ′ -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 α ′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.

Bonus scaling and BCFW inN=7supergravity

“…Applications of BCFW recursion to string amplitudes have demonstrated improved large z scaling compared to field theory amplitudes in certain kinematic regimes [17,18]. This not only validates the construction of a "bad shift" recursion formula without the requirement of N = 7 supersymmetry, but also enables the application of our previous argument to pursue even better termby-term large z bonus scaling.…”

Exact coefficients for higher dimensional operators with sixteen supersymmetries

“…For example at six points two F 4 operators must generate exactly the same local polynomial as (F − ) 2 (F + ) 4 , and thus the coefficient of the latter must be the opposite of the coefficient of this polynomial. This is indeed exemplified by the DBI action as discussed in [27,28]. We will show that this will allow us to determine the exact coefficient for MHV operators with arbitrary multiplicity.…”

Non-abelian Z-theory: Berends-Giele recursion for the α ′-expansion of disk integrals

“…Given that BCFW on-shell recursions [97] can in principle be applied string amplitudes [98][99][100], it would be interesting to relate the Berends-Giele recursion for Z-theory amplitudes to BCFW methods.…”