Abstract
The Grassmannian formulation of \( \mathcal{N}=4 \) super Yang-Mills theory expresses tree-level scattering amplitudes as linear combinations of residues from certain contour integrals. BCFW bridge decompositions using adjacent transpositions simplify the evaluation of individual residues, but orientation information is lost in the process. We present a straightforward algorithm to compute relative orientations between the resulting coordinate charts, and we show how to generalize the technique for charts corresponding to sequences of any not-necessarily-adjacent transpositions. As applications of these results, we demonstrate the existence of a signed boundary operator that manifestly squares to zero and prove via our algorithm that any residues appearing in the tree amplitude sum are decorated with appropriate signs so all poles that appear twice cancel exactly, not just mod 2 as in previous works. We also identify other non-physical poles in the boundary of Grassmannian representations of the amplitude and justify their removal so that the final result contains only physical local poles.
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Olson, T.M. Orientations of BCFW charts on the Grassmannian. J. High Energ. Phys. 2015, 120 (2015). https://doi.org/10.1007/JHEP08(2015)120
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DOI: https://doi.org/10.1007/JHEP08(2015)120