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arXiv · 2606.18331

Meromorphic amplitudes from 3-dimensional supersymmetry

Federico Ambrosino·Nathan Haouzi
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Abstract

We establish a new connection between supersymmetric theories and scattering amplitudes. We show that the Coon amplitude coincides with the 3d $\mathcal{N}=2$ half-index of the XYZ model with nontrivial boundary conditions. Our 3d theory, intrinsically defined in the UV, flows to a sigma model in the IR whose partition function is the Veneziano amplitude. Crossing symmetry is realized as a consequence of 3d $\mathcal{N}=2$ mirror symmetry between XYZ and SQED. We use this correspondence to construct a meromorphic modification of the Coon amplitude by promoting the long-standing dressing factor $\mathfrak{q}^{ST}$ responsible for a branch cut to an elliptic completion thereof. This illustrates that one does not have to give up single-valuedness to achieve positivity at the physical poles.

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Federico Ambrosino, Nathan Haouzi. 2026-06-16. Meromorphic amplitudes from 3-dimensional supersymmetry. https://arxiv.org/abs/2606.18331

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