2025/05/06 by Cortes, Veronica Calvo, Yassine El Maazouz, Subramanya Hegde +4 · 1 citation
Physics and Astronomy · Mathematics · #Electromagnetic Scattering and Analysis #Mathematics and Applications #Algebraic and Geometric Analysis
paper · pdf · doi:10.48550/arxiv.2505.03705
We present a formulation of the three- and four-point amplitudes on the Coulomb branch of N=4 SYM as integrals over the symplectic Grassmannian. We demonstrate that their kinematic spaces are equivalent to symplectic Grassmannians SpGr(n,2n). For the three-point case, we express the amplitude as an integral over the symplectic Grassmannian in a specific little group frame. In the four-point case, we show that the integral yields the amplitude up to a known kinematic factor. Building on the four-dimensional analysis, we also express the six-dimensional N = (1,1) SYM amplitude in terms of four-dimensional variables in a form that makes its symplectic Grassmannian structure manifest.