# Unraveling L_{n,k}: Grassmannian Kinematics

## TL;DR

This paper develops a method to identify and analyze leading singularities in N=4 super Yang-Mills theory using Grassmannian integrals, revealing new structures at tree, one-loop, and higher loops.

## Contribution

It provides a systematic way to identify residues corresponding to leading singularities in Grassmannian integrals, including explicit calculations at various loop levels and new kinematic structures.

## Key findings

- Explicit identification of all tree and one-loop leading singularities.
- Analysis of two-loop and four-loop leading singularities.
- Discovery of a new kinematic structure involving double square roots.

## Abstract

It was recently proposed that the leading singularities of the S-Matrix of N = 4 super Yang-Mills theory arise as the residues of a contour integral over a Grassmannian manifold, with space-time locality encoded through residue theorems generalizing Cauchy's theorem to more than one variable. We provide a method to identify the residue corresponding to any leading singularity, and we carry this out very explicitly for all leading singularities at tree level and one-loop. We also give several examples at higher loops, including all generic two-loop leading singularities and an interesting four-loop object. As a special case we consider a 12-pt N^4MHV leading singularity at two loops that has a new kinematic structure involving double square roots. Our analysis results in a simple picture for how the topological structure of loop graphs is reflected in various substructures within the Grassmannian.