Binary geometries, generalized particles and strings, and cluster algebras
Nima Arkani–Hamed, Song He, Thomas Lam, Hugh Thomas
Abstract
The authors study the fundamental properties of scattering amplitudes of particles in any spacetime dimension. They introduce binary geometries, giving a completely rigid geometric realization of the combinatorics of generalized associahedra attached to any Dynkin diagram. Furthermore, they define open and closed ``cluster string integrals'', which provide a generalization of particle and string scattering amplitudes, and enjoy remarkable factorization properties at finite ${\ensuremath{\alpha}}^{\ensuremath{'}}$.
Topics & Concepts
GeneralizationFactorizationScattering amplitudeRealization (probability)String (physics)PhysicsString theoryBinary numberDimension (graph theory)Space (punctuation)DiagramTheoretical physicsPure mathematicsMathematicsScatteringMathematical physicsQuantum mechanicsMathematical analysisComputer scienceAlgorithmStatisticsArithmeticOperating systemAlgebraic structures and combinatorial modelsBlack Holes and Theoretical PhysicsAdvanced Combinatorial Mathematics