General Split Helicity Gluon Tree Amplitudes in Open Twistor String Theory

TL;DR

This paper explicitly evaluates split helicity gluon tree amplitudes in open twistor string theory, demonstrating their agreement with gauge theory and satisfying BCFW recurrence relations, thus bridging string theory and gauge theory results.

Contribution

It provides a detailed computation of split helicity gluon amplitudes in twistor string theory, confirming their consistency with gauge theory and elucidating the pole structure via link variables.

Findings

Amplitudes satisfy BCFW recurrence relations.

Explicit evaluation matches gauge theory results.

Residue analysis clarifies pole contributions.

Abstract

We evaluate all split helicity gluon tree amplitudes in open twistor string theory. We show that these amplitudes satisfy the BCFW recurrence relations restricted to the split helicity case and, hence, that these amplitudes agree with those of gauge theory. To do this we make a particular choice of the sextic constraints in the link variables that determine the poles contributing to the contour integral expression for the amplitudes. Using the residue theorem to re-express this integral in terms of contributions from poles at rational values of the link variables, which we determine, we evaluate the amplitudes explicitly, regaining the gauge theory results of Britto et al.