Hedgehog bases for An cluster polylogarithms and an application to six-point amplitudes

Parker, Daniel E.; Scherlis, Adam; Spradlin, Marcus; Volovich, Anastasia

doi:10.1007/JHEP11(2015)136

Title: Hedgehog bases for A_n cluster polylogarithms and an application to six-point amplitudes

Journal Article · Fri Nov 20 00:00:00 EST 2015 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP11(2015)136· OSTI ID:1435155

Parker, Daniel E. ^[1]; Scherlis, Adam ^[1]; Spradlin, Marcus ^[1]; Volovich, Anastasia ^[1]

Brown Univ., Providence, RI (United States)

Multi-loop scattering amplitudes in N=4 Yang-Mills theory possess cluster algebra structure. In order to develop a computational framework which exploits this connection, we show how to construct bases of Goncharov polylogarithm functions, at any weight, whose symbol alphabet consists of cluster coordinates on the A_n cluster algebra. As a result, using such a basis we present a new expression for the 2-loop 6-particle NMHV amplitude which makes some of its cluster structure manifest.

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Research Organization:: Brown Univ., Providence, RI (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0010010

OSTI ID:: 1435155

Journal Information:: Journal of High Energy Physics (Online), Vol. 2015, Issue 11; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 18 works

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The cosmic Galois group and extended Steinmann relations for planar N $$ \mathcal{N} $$ = 4 SYM amplitudes Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2019-03749	text	January 2019
The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2019-02565	text	January 2019
Evidence for a Nonplanar Amplituhedron Bern, Zvi; Herrmann, Enrico; Litsey, Sean arXiv https://doi.org/10.48550/arxiv.1512.08591	text	January 2015
Gravity On-shell Diagrams Herrmann, Enrico; Trnka, Jaroslav arXiv https://doi.org/10.48550/arxiv.1604.03479	text	January 2016
Bootstrapping a Five-Loop Amplitude Using Steinmann Relations Caron-Huot, Simon; Dixon, Lance J.; McLeod, Andrew arXiv https://doi.org/10.48550/arxiv.1609.00669	text	January 2016
Prescriptive Unitarity Bourjaily, Jacob L.; Herrmann, Enrico; Trnka, Jaroslav arXiv https://doi.org/10.48550/arxiv.1704.05460	text	January 2017
Rationalizing Loop Integration Bourjaily, Jacob L.; McLeod, Andrew J.; von Hippel, Matt arXiv https://doi.org/10.48550/arxiv.1805.10281	text	January 2018
Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function Golden, John; McLeod, Andrew J. arXiv https://doi.org/10.48550/arxiv.1810.12181	text	January 2018
The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko arXiv https://doi.org/10.48550/arxiv.1906.07116	text	January 2019

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Title: Hedgehog bases for A_n cluster polylogarithms and an application to six-point amplitudes