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

Journal Article · · Journal of High Energy Physics (Online)
 [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)
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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
Citation Metrics:
Cited by: 26 works
Citation information provided by
Web of Science

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Cited By (8)

Yangian invariants and cluster adjacency in $$ \mathcal{N} $$ = 4 Yang-Mills journal October 2019
Six-Gluon amplitudes in planar N$$ \mathcal{N} $$ = 4 super-Yang-Mills theory at six and seven loops journal August 2019
The cosmic Galois group and extended Steinmann relations for planar N $$ \mathcal{N} $$ = 4 SYM amplitudes text January 2019
Six-Gluon Amplitudes in Planar ${\cal N}=4$ Super-Yang-Mills Theory at Six and Seven Loops text January 2019
The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes text January 2019
The Sklyanin Bracket and Cluster Adjacency at All Multiplicity text January 2019
PolyLogTools - Polylogs for the masses text January 2019
The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes text January 2019

Figures / Tables (13)

Figure 1(p. 8)figure Figure 1
Figure 2(p. 13)figure Figure 2
Figure 3(p. 15)figure Figure 3
Figure 4(p. 16)figure Figure 4
Figure 5(p. 19)figure Figure 5
Figure 6(p. 21)figure Figure 6
Table 1(p. 43)table Table 1
Table 2(p. 44)table Table 2
Table 3(p. 45)table Table 3
Table 4(p. 46)table Table 4
Figure 7(p. 53)figure Figure 7
Table 5(p. 60)table Table 5
Table 6(p. 61)table Table 6

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Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Scattering Amplitudes
Supersymmetric Gauge Theory