All Conjugate-Maximal-Helicity-Violating Amplitudes from Topological Open String Theory in Twistor Space

It has recently been proposed that the D-instanton expansion of the open topological $B$ model on ${\mathbb{P}}^{3|4}$ is equivalent to the perturbative expansion of the maximally supersymmetric Yang-Mills theory in four dimensions. In this letter we show how to construct the gauge theory results for all $n$-point conjugate-maximal-helicity-violating amplitudes by computing the integral over the moduli space of curves of degree $n-3$ in ${\mathbb{P}}^{3|4}$, providing strong support to the string theory construction.