Anatomy of the Amplituhedron

Understand

We initiate a comprehensive investigation of the geometry of the amplituhedron, a recently found geometric object whose volume calculates the integrand of scattering amplitudes in planar N=4 SYM theory.

• We do so by introducing and studying its stratification, focusing on four-point amplitudes.
• The new stratification exhibits interesting combinatorial properties and positivity is neatly captured by permutations.
• As explicit examples, we find all boundaries for the two and three loop amplitudes and related geometries.