HET- seminar: Anders Schreiber

Speaker: Anders Schreiber

Title: Cluster Adjacency in N=4 Super Yang-Mills Theory

Abstract: Grassmannian cluster algebras have been found to play a significant role in scattering amplitudes of planar N=4 supersymmetric Yang-Mills Theory (SYM). Scattering amplitudes in particular exhibit cluster algebraic properties in many aspects: in their integrands, symbol alphabets, and cobrackets.

Recently Drummond, Foster, and Gurdogan suggested various conjectures regarding the cluster algebraic structure of scattering amplitudes in N=4 SYM. For n-particle scattering at tree-level it is conjectured that Yangian invariants, appearing in the BCFW expansion of the scattering amplitude, each have poles that appear in a common cluster and are thus cluster adjacent. At loop-level it conjectured that adjacent entries in the symbol are cluster adjacent. Furthermore, beyond MHV amplitudes, it is conjectured that the final entry of each term of the (2L-1,1) coproduct (at L loops) is cluster adjacent to the poles of the Yangian invariant multiplying that term in the coproduct. These conjectures have significant support for n= 6,7, where the associated cluster algebra is of finite type.

In my talk, we explore a new tool that can be used to check these conjectures when n  8, where the Gr(4,n) cluster algebras are infinite. This tool is known as the Sklyanin bracket and is conjectured to give a numerical test of whether any two cluster or Plucker coordinates are cluster adjacent. We use this tool to explore the cluster adjacency of tree-level Yangian invariants and NMHV amplitudes at one-loop. We find agreement with the conjectures proposed by Drummond, Foster, and Gurdogan.