We use geometric Landau analysis to determine the singularity structure of four-point, one-cycle negative geometries in 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 ∞ 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.
@article{arxiv.2604.22683,
title = {Landau Analysis of One-Cycle Negative Geometries},
author = {Shruti Paranjape and Marcos Skowronek and Marcus Spradlin and Anastasia Volovich and He-Chen Weng},
journal= {arXiv preprint arXiv:2604.22683},
year = {2026}
}