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 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.
- 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:
- AC02-76SF00515
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); 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. https://doi.org/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. https://doi.org/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)},
number = 1,
volume = 2019,
place = {United States},
year = {2019},
month = {1}
}
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Figure 1: All possible triangulations of the pentagon. Mutating on the red chord moves you clockwise around the figure.
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Works referencing / citing this record:
Yangian invariants and cluster adjacency in $$ \mathcal{N} $$ = 4 Yang-Mills
journal, October 2019
- Mago, Jorge; Schreiber, Anders; Spradlin, Marcus
- Journal of High Energy Physics, Vol. 2019, Issue 10
The cosmic Galois group and extended Steinmann relations for planar N $$ \mathcal{N} $$ = 4 SYM amplitudes
text, January 2019
- Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Six-Gluon Amplitudes in Planar ${\cal N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
text, January 2019
- Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes
text, January 2019
- Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
text, January 2019
- Golden, John; McLeod, Andrew J.; Spradlin, Marcus
- arXiv
The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes
text, January 2019
- Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko
- arXiv
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