# A connection between $\mathcal{R}$-invariants and Yang-Baxter $R$-operators in $\mathcal{N}=4$ super-Yang-Mills theory

## TL;DR

This paper demonstrates how to solve the BCFW recursion in $ ext{N}=4$ super-Yang-Mills theory using Yang-Baxter $R$-operators, explicitly linking $ ext{R}$-invariants with these operators in the NMHV sector.

## Contribution

It introduces a novel method of expressing $ ext{R}$-invariants through chains of $R$-operators, connecting integrability structures with scattering amplitudes.

## Key findings

- Explicit expressions for $ ext{R}$-invariants in terms of $R$-operator chains
- Solution of BCFW recursion using Yang-Baxter $R$-operators
- New insights into the structure of NMHV amplitudes

## Abstract

The BCFW recursion relation in $\mathcal{N}=4$ super-Yang-Mills theory is solved using Yang-Baxter $R$-operators in the NMHV sector. Explicit expressions for $\mathcal{R}$-invariants are obtained in terms of the chains of $R$-operators acting on an appropriate basic state.