Logarithms and Volumes of Polytopes

Understand

Describing the geometry of the dual amplituhedron without reference to a particular triangulation is an open problem.

• In this note we introduce a new way of determining the volume of the tree-level NMHV dual amplituhedron.
• We show that certain contour integrals of logarithms serve as natural building blocks for computing this volume as well as the volumes of general polytopes in any dimension.
• These building blocks encode the geometry of the underlying polytopes in a triangulation-independent way, and make identities between different representations of the amplitudes manifest.