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arXiv · 2505.03705

Symplectic Grassmannian description of the Coulomb branch three and four point amplitudes

Veronica Calvo Cortes·Yassine El Maazouz·Subramanya Hegde·Amit Suthar
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Abstract

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.

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Veronica Calvo Cortes, Yassine El Maazouz, Subramanya Hegde, Amit Suthar. 2025-05-06. Symplectic Grassmannian description of the Coulomb branch three and four point amplitudes. https://arxiv.org/abs/2505.03705

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