The Sklyanin bracket and cluster adjacency at all multiplicity

Golden, John; McLeod, Andrew J.; Spradlin, Marcus; Volovich, Anastasia

doi:10.1007/JHEP03(2019)195

The Sklyanin bracket and cluster adjacency at all multiplicity

Journal Article · Fri Mar 29 00:00:00 EDT 2019 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP03(2019)195· OSTI ID:1596975

Golden, John ^[1]; McLeod, Andrew J. ^[2]; Spradlin, Marcus ^[3]; Volovich, Anastasia ^[3]

Univ. of Michigan, Ann Arbor, MI (United States); Brown University
Univ. of Copenhagen (Denmark). The Niels Bohr Inst.
Brown Univ., Providence, RI (United States)

We argue that the Sklyanin Poisson bracket on Gr(4,n) can be used to efficiently test whether an amplitude in planar $${\cal{N}}=4$$ 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.

View Accepted Manuscript (DOE)

Research Organization:: Brown Univ., Providence, RI (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

Grant/Contract Number:: SC0010010

OSTI ID:: 1596975

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 3 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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