All-loop cuts from the Amplituhedron

Understand

The definition of the amplituhedron in terms of sign flips involves both one-loop constraints and the "mutual positivity" constraint.

• To gain an understanding of the all-loop integrand of $\mathcal{N}=4$ sYM requires understanding the crucial role played by mutual positivity.
• This paper is an attempt towards developing a procedure to introduce the complexities of mutual positivity in a systematic and controlled manner.
• As the first step in this procedure, we trivialize these constraints and understand the geometry underlying the remaining constraints to all loops and multiplicities.