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

Abstract

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 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 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 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:
 [1];  [2]
  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)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1493350
Grant/Contract Number:  
AC02-76SF00515
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 1029-8479
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 seven-particle 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 seven-particle 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 seven-particle 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 seven-particle 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 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.},
doi = {10.1007/jhep01(2019)017},
journal = {Journal of High Energy Physics (Online)},
issn = {1029-8479},
number = 1,
volume = 2019,
place = {United States},
year = {2019},
month = {1}
}

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Cited by: 2 works
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Figures / Tables:

Figure 1 Figure 1: All possible triangulations of the pentagon. Mutating on the red chord moves you clockwise around the figure.

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