In recent years the use of intersections of twisted forms for scattering amplitudes has added a rich mathematical tool in the calculation and understanding of different amplitudes within quantum field theories from CHY formulae to string theory. It has been shown that using string theory amplitudes one can construct the twisted forms associated to different types of QFT amplitudes (Yang Mills, GR, etc).
However, among all of the known amplitudes there is a gap for the twisted forms of the Einstein Yang-Mills amplitude (EYM). In string theory this amplitude is computed on the disk world-sheet in contrast to intersection theory and CHY formalism which use the Riemann sphere. Therefore, one cannot use standard string theory as a guideline for constructing twisted forms of EYM.
After introducing the necessary background on twisted intersection theory I am going to present our geometrical solution to this problem by embedding the disk onto sphere and calculating the resulting mixed closed-open string amplitude. We are able to extract a pair of twisted forms associated to the EYM . We check our result by showing that the intersection of the constructed twisted forms in \alpha' -> infinity limit will give the CHY formula for the EYM. This talk is based on arXiv:2201.00837.