Tropical Grassmannians, cluster algebras and scattering amplitudes
J. M. Drummond, Jack Foster, Ömer Gürdoğan, Chrysostomos Kalousios
Abstract
A bstract We provide a cluster-algebraic approach to the computation of the recently introduced generalised biadjoint scalar amplitudes related to Grassmannians Gr( k, n ). A finite cluster algebra provides a natural triangulation for the tropical Grassmannian whose volume computes the scattering amplitudes. Using this method one can construct the entire colour-ordered amplitude via mutations starting from a single term.
Topics & Concepts
Cluster algebraGrassmannianScattering amplitudeScalar (mathematics)MathematicsComputationScatteringCluster (spacecraft)AmplitudeAlgebraic numberTriangulationAlgebra over a fieldPure mathematicsCombinatoricsPhysicsMathematical analysisComputer scienceGeometryAlgorithmQuantum mechanicsIsing modelProgramming languageAlgebraic structures and combinatorial modelsNonlinear Waves and SolitonsAdvanced Topics in Algebra