🔗 Amplituhedron

🔗 Mathematics 🔗 Physics

An amplituhedron is a geometric structure introduced in 2013 by Nima Arkani-Hamed and Jaroslav Trnka. It enables simplified calculation of particle interactions in some quantum field theories. In planar N = 4 supersymmetric Yang–Mills theory, also equivalent to the perturbative topological B model string theory in twistor space, an amplituhedron is defined as a mathematical space known as the positive Grassmannian.

Amplituhedron theory challenges the notion that spacetime locality and unitarity are necessary components of a model of particle interactions. Instead, they are treated as properties that emerge from an underlying phenomenon.

The connection between the amplituhedron and scattering amplitudes is at present a conjecture that has passed many non-trivial checks, including an understanding of how locality and unitarity arise as consequences of positivity. Research has been led by Nima Arkani-Hamed. Edward Witten described the work as "very unexpected" and said that "it is difficult to guess what will happen or what the lessons will turn out to be".