The Sklyanin Bracket and Cluster Adjacency at All Multiplicity

Abstract

We argue that the Sklyanin Poisson bracket on Gr(4,n) can be used to efficiently test whether an amplitude in planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory satisfies cluster adjacency. We use this test to show that cluster adjacency is satisfied by all one- and two-loop MHV amplitudes in this theory, once suitably regulated. Using this technique we also demonstrate that cluster adjacency implies the extended Steinmann relations at all particle multiplicities.

25 pages; v2: added reference

References in corpus (10)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Hexagon Wilson loop = six-gluon MHV amplitude
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Bootstrapping an NMHV amplitude through three loops
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• A Cluster Bootstrap for Two-Loop MHV Amplitudes
• Multi-Loop Positivity of the Planar $\mathcal{N}=4$ SYM Six-Point Amplitude
• An analytic result for the two-loop seven-point MHV amplitude in N=4 SYM
• A simple collinear limit of scattering amplitudes at strong coupling
• Cluster Algebras and the Positive Grassmannian

Cited by in corpus (2)

• Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
• Antipodal Symmetry of Two-Loop MHV Amplitudes