Cluster algebras and the subalgebra constructibility of the sevenparticle remainder function
Abstract
We review various aspects of cluster algebras and the ways in which they appear in the study of looplevel amplitudes in planar N=4 supersymmetric YangMills theory. In particular, we highlight the different forms of clusteralgebraic structure that appear in this theory’s twoloop 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 A _{2} or A _{3} 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 sevenparticle kinematics, where we show that the nonclassical part of the twoloop MHV amplitude is also constructible out of functions evaluated on the D _{5} and A _{5} subalgebras of Gr( _{4, 7}), and that these decompositions are themselves decomposable in terms of the same A _{4} 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.
 Authors:

 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
 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)
 Publication Date:
 Research Org.:
 SLAC National Accelerator Lab., Menlo Park, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1493350
 Grant/Contract Number:
 AC0276SF00515
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Volume: 2019; Journal Issue: 1; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Scattering Amplitudes; Supersymmetric Gauge Theory
Citation Formats
Golden, John, and McLeod, Andrew J. Cluster algebras and the subalgebra constructibility of the sevenparticle remainder function. United States: N. p., 2019.
Web. doi:10.1007/jhep01(2019)017.
Golden, John, & McLeod, Andrew J. Cluster algebras and the subalgebra constructibility of the sevenparticle remainder function. United States. doi:10.1007/jhep01(2019)017.
Golden, John, and McLeod, Andrew J. Thu .
"Cluster algebras and the subalgebra constructibility of the sevenparticle remainder function". United States. doi:10.1007/jhep01(2019)017. https://www.osti.gov/servlets/purl/1493350.
@article{osti_1493350,
title = {Cluster algebras and the subalgebra constructibility of the sevenparticle remainder function},
author = {Golden, John and McLeod, Andrew J.},
abstractNote = {We review various aspects of cluster algebras and the ways in which they appear in the study of looplevel amplitudes in planar N=4 supersymmetric YangMills theory. In particular, we highlight the different forms of clusteralgebraic structure that appear in this theory’s twoloop 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 sevenparticle kinematics, where we show that the nonclassical part of the twoloop 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.},
doi = {10.1007/jhep01(2019)017},
journal = {Journal of High Energy Physics (Online)},
issn = {10298479},
number = 1,
volume = 2019,
place = {United States},
year = {2019},
month = {1}
}
Web of Science
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