<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>decoupling, Kleiss-Kuijf and Bern-Carrasco-Johansson relations in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math>super Yang-Mills

By using the Britto-Cachazo-Feng-Witten recursion relation of $\mathcal{N}=4$ super Yang-Mills theory, we proved the color reflection, $U(1)$ decoupling, Kle...