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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 non-local poles cancel exactly, not just mod 2 as in previous works.
We study leading singularities of scattering amplitudes which are obtained as residues of an integral over a Grassmannian manifold. We recursively do the transformation from twistors to momentum twistors and obtain an iterative formula for Yangian in
We construct an off-shell extension of cubic interaction vertices between massless bosonic Higher Spin fields on a flat background which can be obtained from perturbative bosonic string theory. We demonstrate how to construct higher quartic interacti
The goal of the present note is to understand whether it is possible to define interacting quantum field theory in global anti de Sitter space-time with Lorentzian signature, in its covering space-time (whose time coordinate is not periodic) and in i
We study the scattering problem in the static patch of de Sitter space, i.e. the problem of field evolution between the past and future horizons of a de Sitter observer. We formulate the problem in terms of off-shell fields in Poincare coordinates. T
The number of planar Eulerian maps with n edges is well-known to have a simple expression. But what is the number of planar Eulerian orientations with n edges? This problem appears to be difficult. To approach it, we define and count families of subs