Positive Geometries for all Scalar Theories from Twisted Intersection Theory

Abstract

We show that accordiohedra furnish polytopes which encode amplitudes for all massive scalar field theories with generic interactions. This is done by deriving integral formulae for the Feynman diagrams at tree level and integrands at one loop level in the planar limit using the twisted intersection theory of convex realizations of the accordiohedron polytopes.

v2: Corrected typos and added references - published version

References in corpus (4)

• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
• Two-Loop Scattering Amplitudes from the Riemann Sphere

Cited by in corpus (15)

• Decomposition of Feynman Integrals by Multivariate Intersection Numbers
• Intersection Numbers from Higher-order Partial Differential Equations
• Algebraic branch points at all loop orders from positive kinematics and wall crossing
• Soft Gravity by Squaring Soft QED on the Celestial Sphere
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
• Celebrating Loday's Associahedron
• Gauge and Gravity Amplitudes on the Celestial Sphere
• On Polytopes and Generalizations of the KLT Relations
• Open associahedra and scattering forms
• Weights, Recursion relations and Projective triangulations for Positive Geometry of scalar theories
• One-loop integrand from generalised scattering equations
• Double Soft Theorem for Generalised Biadjoint Scalar Amplitudes
• Geometric Recursion from Polytope Triangulations and Twisted Homology
• Co-homology of Differential Forms and Feynman diagrams
• BCFW like recursion for Deformed Associahedron