Landau Analysis of One-Cycle Negative Geometries

TL;DR

This paper employs geometric Landau analysis to identify the singularity structure of specific four-point geometries in super-Yang-Mills theory, revealing singularities only at three points across all loop orders.

Contribution

It demonstrates that the singularities of these geometries are confined to three points, providing a foundation for non-perturbative resummation at next-to-leading order.

Findings

Singularities only at z=-1, 0, and infinity for all loop orders.

Recursive Landau diagram analysis confirms the singularity structure.

Advances understanding of non-perturbative aspects in super-Yang-Mills theory.

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.