Built on

O. Steinmann, Über den Zusammenhang zwischen den Wightmanfunktionen und der retardierten Kommutatoren , Helv. Physica Acta 33
1960
Earlier work this paper cites.
O. Steinmann, Wightman-Funktionen und retardierten Kommutatoren. II , Helv. Physica Acta 33
1960
Earlier work this paper cites.
K. E. Cahill and H. P. Stapp, Optical Theorems and Steinmann Relations , Annals Phys. 90
1975
Earlier work this paper cites.
E. K. Sklyanin, Some algebraic structures connected with the Yang-Baxter equation , Funct. Anal. Appl. 16
1982
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar and D. A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits , Nucl. Phys. B425
1994
Earlier work this paper cites.
M. Gekhtman, M. Z. Shapiro and A. D. Vainshtein, Cluster algebras and poisson geometry , Moscow Mathematical Journal 3
2003
Earlier work this paper cites.
Z. Bern, L. J. Dixon and V. A. Smirnov, Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond , Phys. Rev. D72
2005
Earlier work this paper cites.
N. Beisert, B. Eden and M. Staudacher, Transcendentality and Crossing , J. Stat. Mech. 0701
2007
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. A. Kosower, R. Roiban, M. Spradlin, C. Vergu et al., The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory , Phys. Rev. D78
Original
2008
Earlier work this paper cites.
V. V. Fock and A. B. Goncharov, Cluster ensembles, quantization and the dilogarithm , Ann. Sci. Éc. Norm. Supér. (4) 42
2009
Earlier work this paper cites.
J. M. Drummond, J. Henn, G. P. Korchemsky and E. Sokatchev, Hexagon Wilson loop = six-gluon MHV amplitude , Nucl. Phys. B815
Original
2009
Earlier work this paper cites.
L. F. Alday, J. Maldacena, A. Sever and P. Vieira, Y-system for Scattering Amplitudes , J. Phys. A43
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 super Yang-Mills , JHEP 12
Original
2011
Earlier work this paper cites.
L. F. Alday, D. Gaiotto and J. Maldacena, Thermodynamic Bubble Ansatz , JHEP 09
Original
2011
Earlier work this paper cites.
G. Yang, A simple collinear limit of scattering amplitudes at strong coupling , JHEP 03
Original
2011
Earlier work this paper cites.
S. Caron-Huot and S. He, Jumpstarting the All-Loop S-Matrix of Planar N=4 Super Yang-Mills , JHEP 07
Original
2012
Earlier work this paper cites.

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2019

The Sklyanin Bracket and Cluster Adjacency at All Multiplicity

Golden, John, McLeod, Andrew J., Spradlin, Marcus et al.

Understand

We argue that the Sklyanin Poisson bracket on Gr(4,n) can be used to efficiently test whether an amplitude in planar ${\cal{N}}=4$ supersymmetric Yang-Mills theory satisfies cluster adjacency.

We use this test to show that cluster adjacency is satisfied by all one- and two-loop MHV amplitudes in this theory, once suitably regulated.
Using this technique we also demonstrate that cluster adjacency implies the extended Steinmann relations at all particle multiplicities.

Built on

O. Steinmann, Über den Zusammenhang zwischen den Wightmanfunktionen und der retardierten Kommutatoren , Helv. Physica Acta 33
1960
Earlier work this paper cites.
O. Steinmann, Wightman-Funktionen und retardierten Kommutatoren. II , Helv. Physica Acta 33
1960
Earlier work this paper cites.
K. E. Cahill and H. P. Stapp, Optical Theorems and Steinmann Relations , Annals Phys. 90
1975
Earlier work this paper cites.
E. K. Sklyanin, Some algebraic structures connected with the Yang-Baxter equation , Funct. Anal. Appl. 16
1982
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar and D. A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits , Nucl. Phys. B425
1994
Earlier work this paper cites.
M. Gekhtman, M. Z. Shapiro and A. D. Vainshtein, Cluster algebras and poisson geometry , Moscow Mathematical Journal 3
2003
Earlier work this paper cites.
Z. Bern, L. J. Dixon and V. A. Smirnov, Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond , Phys. Rev. D72
2005
Earlier work this paper cites.
N. Beisert, B. Eden and M. Staudacher, Transcendentality and Crossing , J. Stat. Mech. 0701
2007
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. A. Kosower, R. Roiban, M. Spradlin, C. Vergu et al., The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory , Phys. Rev. D78
Original
2008
Earlier work this paper cites.
V. V. Fock and A. B. Goncharov, Cluster ensembles, quantization and the dilogarithm , Ann. Sci. Éc. Norm. Supér. (4) 42
2009
Earlier work this paper cites.
J. M. Drummond, J. Henn, G. P. Korchemsky and E. Sokatchev, Hexagon Wilson loop = six-gluon MHV amplitude , Nucl. Phys. B815
Original
2009
Earlier work this paper cites.
L. F. Alday, J. Maldacena, A. Sever and P. Vieira, Y-system for Scattering Amplitudes , J. Phys. A43
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 super Yang-Mills , JHEP 12
Original
2011
Earlier work this paper cites.
L. F. Alday, D. Gaiotto and J. Maldacena, Thermodynamic Bubble Ansatz , JHEP 09
Original
2011
Earlier work this paper cites.
G. Yang, A simple collinear limit of scattering amplitudes at strong coupling , JHEP 03
Original
2011
Earlier work this paper cites.
S. Caron-Huot and S. He, Jumpstarting the All-Loop S-Matrix of Planar N=4 Super Yang-Mills , JHEP 07
Original
2012
Earlier work this paper cites.