Built on

A. Suslin, K 3 K_{3} of a field and the Bloch group
1990
Earlier work this paper cites.
A. B. Goncharov, “Polylogarithms and motivic Galois group,” Proc. Sympos. Pure Math. 55, Part 2, Amer. Math. Soc., Providence, 1994, 43–96
1994
Earlier work this paper cites.
A. Goncharov, “Geometry of configurations, polylogarithms, and motivic cohomology”, Adv. Math
1995
Earlier work this paper cites.
Providence, RI: American Mathematical Society (AMS), 2000
S. J. Bloch, Higher regulators, algebraic K K -theory, and zeta functions of elliptic curves · 2000
Earlier work this paper cites.
A.B. Goncharov, “Galois symmetries of fundamental groupoids and noncommutative geometry”, Duke Math. J. 128
2005
Earlier work this paper cites.
V. V. Fock and A. B. Goncharov, “Cluster ensembles, quantization and the dilogarithm”, Ann. Sci. Éc. Norm. Supér. (4)
2009
Earlier work this paper cites.
P. Heslop and V. V. Khoze, “Analytic Results for MHV Wilson Loops,” JHEP 1011
Original
2010
Earlier work this paper cites.
V. Del Duca, C. Duhr and V. A. Smirnov, “An Analytic Result for the Two-Loop Hexagon Wilson Loop in 𝒩 = \mathcal{N}= 4 SYM,” JHEP 1003
Original
2010
Earlier work this paper cites.
V. Del Duca, C. Duhr and V. A. Smirnov, “The Two-Loop Hexagon Wilson Loop in 𝒩 = 4 \mathcal{N}=4 SYM,” JHEP 1005
Original
2010
Earlier work this paper cites.
A. B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, “Classical Polylogarithms for Amplitudes and Wilson Loops,” Phys. Rev. Lett. 105
Original
2010
Earlier work this paper cites.
S. Caron-Huot, “Superconformal symmetry and two-loop amplitudes in planar 𝒩 = 4 \mathcal{N}=4 super Yang-Mills,” JHEP 1112
Original
2011
Earlier work this paper cites.

Similar

P. Heslop and V. V. Khoze, “Wilson Loops @ 3-Loops in Special Kinematics,” JHEP 1111
Original
2011
Cited alongside, same era.
L. J. Dixon, J. M. Drummond and J. M. Henn, “Bootstrapping the three-loop hexagon,” JHEP 1111
Original
2011
Cited alongside, same era.
A. Prygarin, M. Spradlin, C. Vergu and A. Volovich, “All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology,” Phys. Rev. D 85
Original
2012
Cited alongside, same era.
L. J. Dixon, C. Duhr and J. Pennington, “Single-valued harmonic polylogarithms and the multi-Regge limit,” JHEP 1210
Original
2012
Cited alongside, same era.
T. Goddard, P. Heslop and V. V. Khoze, “Uplifting Amplitudes in Special Kinematics,” JHEP 1210

Then

G. Papathanasiou, “Hexagon Wilson Loop OPE and Harmonic Polylogarithms,” JHEP 1311
Original
2013
Later among the works it cites.
S. Caron-Huot and S. He, “Three-loop octagons and n n -gons in maximally supersymmetric Yang-Mills theory,” JHEP 1308
Original
2013
Later among the works it cites.
J. Golden and M. Spradlin, “The differential of all two-loop MHV amplitudes in 𝒩 \mathcal{N} = 4 Yang-Mills theory,” JHEP 1309
Original
2013
Later among the works it cites.
L. J. Dixon, J. M. Drummond, M. von Hippel and J. Pennington, “Hexagon functions and the three-loop remainder function,” JHEP 1312
Original
2013
Later among the works it cites.
Talk by J. Golden at the SCGP workshop on The Geometry and Physics of Scattering Amplitudes

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2014

Cluster Polylogarithms for Scattering Amplitudes

Golden, John, Paulos, Miguel F., Spradlin, Marcus et al.

Understand

Motivated by the cluster structure of two-loop scattering amplitudes in N=4 Yang-Mills theory we define "cluster polylogarithm functions".

We find that all such functions of weight 4 are made up of a single simple building block associated to the A_2 cluster algebra.
Adding the requirement of locality on generalized Stasheff polytopes, we find that these A_2 building blocks arrange themselves to form a unique function associated to the A_3 cluster algebra.
This A_3 function manifests all of the cluster algebraic structure of the two-loop n-particle MHV amplitudes for all n, and we use it to provide an explicit representation for the most complicated part of the n=7 amplitude as an example.

Built on

A. Suslin, K 3 K_{3} of a field and the Bloch group
1990
Earlier work this paper cites.
A. B. Goncharov, “Polylogarithms and motivic Galois group,” Proc. Sympos. Pure Math. 55, Part 2, Amer. Math. Soc., Providence, 1994, 43–96
1994
Earlier work this paper cites.
A. Goncharov, “Geometry of configurations, polylogarithms, and motivic cohomology”, Adv. Math
1995
Earlier work this paper cites.
Providence, RI: American Mathematical Society (AMS), 2000
S. J. Bloch, Higher regulators, algebraic K K -theory, and zeta functions of elliptic curves · 2000
Earlier work this paper cites.
A.B. Goncharov, “Galois symmetries of fundamental groupoids and noncommutative geometry”, Duke Math. J. 128
2005
Earlier work this paper cites.
V. V. Fock and A. B. Goncharov, “Cluster ensembles, quantization and the dilogarithm”, Ann. Sci. Éc. Norm. Supér. (4)
2009
Earlier work this paper cites.
P. Heslop and V. V. Khoze, “Analytic Results for MHV Wilson Loops,” JHEP 1011
Original
2010
Earlier work this paper cites.
V. Del Duca, C. Duhr and V. A. Smirnov, “An Analytic Result for the Two-Loop Hexagon Wilson Loop in 𝒩 = \mathcal{N}= 4 SYM,” JHEP 1003
Original
2010
Earlier work this paper cites.
V. Del Duca, C. Duhr and V. A. Smirnov, “The Two-Loop Hexagon Wilson Loop in 𝒩 = 4 \mathcal{N}=4 SYM,” JHEP 1005
Original
2010
Earlier work this paper cites.
A. B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, “Classical Polylogarithms for Amplitudes and Wilson Loops,” Phys. Rev. Lett. 105
Original
2010
Earlier work this paper cites.
S. Caron-Huot, “Superconformal symmetry and two-loop amplitudes in planar 𝒩 = 4 \mathcal{N}=4 super Yang-Mills,” JHEP 1112
Original
2011
Earlier work this paper cites.