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:

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

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+ Show Author Affiliations

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:

2019-01-03

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