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arXiv · 2604.22683

Landau Analysis of One-Cycle Negative Geometries

Shruti Paranjape·Marcos Skowronek·Marcus Spradlin·Anastasia Volovich·He-Chen Weng
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Abstract

We use geometric Landau analysis to determine the singularity structure of four-point, one-cycle negative geometries in $\mathcal{N}=4$ super-Yang-Mills theory, which represent certain contributions to the logarithm of the four-point amplitude or equivalently the normalized quadrangular Wilson loop with a Lagrangian insertion. By analyzing the relevant Landau diagrams recursively, we prove that this quantity has singularities only at $z=-1,0$ and $\infty$ to all loop orders. This represents a first step towards obtaining a non-perturbative resummation for this quantity at next-to-leading order in the expansion over cycles.

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Shruti Paranjape, Marcos Skowronek, Marcus Spradlin, Anastasia Volovich, He-Chen Weng. 2026-05-06. Landau Analysis of One-Cycle Negative Geometries. https://arxiv.org/abs/2604.22683

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