Positivity Sectors and the Amplituhedron

Understand

We initiate a detailed investigation into the assembly of simple amplituhedron-like building blocks to obtain spaces of physical interest.

• In particular, we describe the geometric process through which the building blocks, which we call positivity sectors, glue together to form the desired geometries.
• Positivity sectors are seen to naturally segment the space describing the Lth power of the one-loop amplitude.
• In this way, we obtain a good understanding of how the geometric complexity of the building blocks can be washed out in the formation of larger spaces.