Cluster algebras and the subalgebra constructibility of the seven-particle remainder function

Journal Article · 03 January 2019 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep01(2019)017 · OSTI ID:1493350

Golden, John ^[1]; McLeod, Andrew J. ^[2]

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1. Univ. of Michigan, Ann Arbor, MI (United States). Leinweber Center for Theoretical Physics and Randall Lab. of Physics; Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics
2. Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; SLAC National Accelerator Lab., Menlo Park, CA (United States); Niels Bohr International Academy, Copenhagen (Denmark)

We review various aspects of cluster algebras and the ways in which they appear in the study of loop-level amplitudes in planar N=4 supersymmetric Yang-Mills theory. In particular, we highlight the different forms of cluster-algebraic structure that appear in this theory’s two-loop MHV amplitudes — considered as functions, symbols, and at the level of their Lie cobracket — and recount how the ‘nonclassical’ part of these amplitudes can be decomposed into specific functions evaluated on the A₂ or A₃ subalgebras of Gr(_{4, n}). We then extend this line of inquiry by searching for other subalgebras over which these amplitudes can be decomposed. We focus on the case of seven-particle kinematics, where we show that the nonclassical part of the two-loop MHV amplitude is also constructible out of functions evaluated on the D₅ and A₅ subalgebras of Gr(_{4, 7}), and that these decompositions are themselves decomposable in terms of the same A₄ function. These nested decompositions take an especially canonical form, which is dictated in each case by constraints arising from the automorphism group of the parent algebra.

• Research Organization: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC02-76SF00515
• OSTI ID: 1493350
• Journal Information: Journal of High Energy Physics (Online), Vol. 2019, Issue 1; ISSN 1029-8479
• Publisher: Springer BerlinCopyright Statement
• Country of Publication: United States
• Language: English