Triangulation of 2-loop MHV Amplituhedron from sign flips Ryota - PowerPoint PPT Presentation

Triangulation of 2-loop MHV Amplituhedron from sign flips Ryota Kojima Sokendai, KEK theory centor Based on RK “Triangulation of 2-loop MHV Amplituhedron from sign flips” 1812.01822 RK and Jaroslav Trnka(UC Davis, QMAP), in progress One-day workshop for QFT and string theory 12/4

Introduction structures underlying scattering amplitudes. The Amplituhedron convex polytope. • no reference to usual field theory notions: feynman diagrams, Lagrangian… Scattering amplitude of Planar N=4 SYM. 2 N. Arkani-Hamed, J. Trnka 2013 • Scattering amplitude: Basic objects in QFT. • Study the scattering amplitudes fascinating geometric • Loosely speaking, this is defined as a generalization of interior of • Canonical form (related to the volume) of the amplituhedron =

• Calculate the scattering amplitude = Construct the canonical form of the amplituhedron: this is purely geometrical problem! • However it is difficult to construct this form of general amplituhedron. 3 has logarithmic singularities on all the boundaries of amplituhedron. The definition of canonical form : Definition of the amplituhedron Ω Ω • One way: Triangulate the general amplituhedron into simple one. • Sum of these forms = canonical form of the full amplituhedron.

Introduction Is there a systematic way to triangulate the general amplituhedron? derive it from a QFT. 4 • Question: • In this work, we obtained that • a systematic way to triangulate the general MHV amplituhedron. • a new formula for 2-loop MHV amplitude that is not obvious how to • new geometry: “log amplituhedron”. • the canonical form of the log amplituhedron = log of the amplitude.

Introduction Definition of the amplituhedron Canonical form and triangulation Amplituhedron from sign flip and triangulation Log amplituhedron Summary 5 Plan