Built on

S. Caron-Huot, L.J. Dixon, F. Dulat, M. von Hippel, A.J. McLeod and G. Papathanasiou, Six-Gluon amplitudes in planar 𝒩 \mathcal{N} = 4 super-Yang-Mills theory at six and seven loops , JHEP 08
Original
1903
Earlier work this paper cites.
S. He, Z. Li and C. Zhang, Two-loop Octagons, Algebraic Letters and Q ¯ \bar{Q} Equations , Phys. Rev. D 101
Original
1911
Earlier work this paper cites.
J. Drummond, J. Foster, O. Gürdogan and C. Kalousios, Algebraic singularities of scattering amplitudes from tropical geometry , JHEP 04
Original
1912
Earlier work this paper cites.
N. Arkani-Hamed, T. Lam and M. Spradlin, Non-perturbative geometries for planar 𝒩 \mathcal{N} = 4 SYM amplitudes , JHEP 03
Original
1912
Earlier work this paper cites.
N. Henke and G. Papathanasiou, How tropical are seven- and eight-particle amplitudes? , JHEP 08
Original
1912
Earlier work this paper cites.
O. Steinmann, Über den zusammenhang zwischen den wightmanfunktionen und den retardierten kommutatoren , Helvetica Physica Acta 33
1960
Earlier work this paper cites.
O. Steinmann, Wightman-funktionen und retardierte kommutatoren. ii , Helvetica Physica Acta 33
1960
Earlier work this paper cites.
K.-T. Chen, Iterated path integrals , Bull. Am. Math. Soc. 83
1977
Earlier work this paper cites.
C. Anastasiou, Z. Bern, L.J. Dixon and D.A. Kosower, Planar amplitudes in maximally supersymmetric Yang-Mills theory , Phys. Rev. Lett. 91
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.
A.B. Goncharov, Galois symmetries of fundamental groupoids and noncommutative geometry , Duke Math. J. 128
2005
Earlier work this paper cites.
A.B. Goncharov et al., Galois symmetries of fundamental groupoids and noncommutative geometry , Duke Mathematical Journal 128
2005
Earlier work this paper cites.
J.S. Scott, Grassmannians and cluster algebras , Proceedings of the London Mathematical Society 92
2006
Earlier work this paper cites.
J.M. Drummond, J. Henn, V.A. Smirnov and E. Sokatchev, Magic identities for conformal four-point integrals , JHEP 01
2007
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.
S. He, Z. Li and C. Zhang, The symbol and alphabet of two-loop NMHV amplitudes from Q ¯ \bar{Q} equations , JHEP 03
Original
2009
Earlier work this paper cites.
J.M. Drummond, J.M. Henn and J. Plefka, Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory , JHEP 05
Original
2009
Earlier work this paper cites.
L.J. Mason and D. Skinner, Dual Superconformal Invariance, Momentum Twistors and Grassmannians , JHEP 11
Original
2009
Earlier work this paper cites.
F. Brown, Multiple zeta values and periods of moduli spaces 𝔪 ¯ 0 , n \overline{\mathfrak{m}}_{0,n} , in Annales scientifiques de l’École Normale Supérieure , vol. 42, pp. 371–489, 2009
2009
Earlier work this paper cites.

Similar

N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the Simplest Quantum Field Theory? , JHEP 09
Original
2010
Cited alongside, same era.
A.B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, Classical Polylogarithms for Amplitudes and Wilson Loops , Phys. Rev. Lett. 105
Original
2010
Cited alongside, same era.
J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory , Nucl. Phys. B828
Original
2010
Cited alongside, same era.
G.P. Korchemsky and E. Sokatchev, Superconformal invariants for scattering amplitudes in N=4 SYM theory , Nucl. Phys. B839
Original
2010
Cited alongside, same era.
J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes , Nucl. Phys. B 826

Then

L.J. Dixon, A.J. McLeod and M. Wilhelm, A Three-Point Form Factor Through Five Loops , JHEP 04
Original
2012
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 08
Original
2013
Later among the works it cites.
A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes , JHEP 05
Original
2013
Later among the works it cites.
L.J. Dixon, J.M. Drummond, C. Duhr, M. von Hippel and J. Pennington, Bootstrapping six-gluon scattering in planar N=4 super-Yang-Mills theory , PoS LL2014
Original
2014
Later among the works it cites.
L.J. Dixon and M. von Hippel, Bootstrapping an NMHV amplitude through three loops , JHEP 10

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2021

The Three-loop MHV Octagon from $\bar{Q}$ equations

Li, Zhenjie, Zhang, Chi

Understand

The $\bar{Q}$ equations, rooted in the dual superconformal anomalies, are a powerful tool for computing amplitudes in planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory.

By using the $\bar{Q}$ equations, we compute the symbol of the first MHV amplitude with algebraic letters -- the three-loop 8-point amplitude (or the octagon remainder function) -- in this theory.
The symbol alphabet for this amplitude consists of 204 independent rational letters and shares the same 18 algebraic letters with the two-loop 8-point NMHV amplitude.

Built on

S. Caron-Huot, L.J. Dixon, F. Dulat, M. von Hippel, A.J. McLeod and G. Papathanasiou, Six-Gluon amplitudes in planar 𝒩 \mathcal{N} = 4 super-Yang-Mills theory at six and seven loops , JHEP 08
Original
1903
Earlier work this paper cites.
S. He, Z. Li and C. Zhang, Two-loop Octagons, Algebraic Letters and Q ¯ \bar{Q} Equations , Phys. Rev. D 101
Original
1911
Earlier work this paper cites.
J. Drummond, J. Foster, O. Gürdogan and C. Kalousios, Algebraic singularities of scattering amplitudes from tropical geometry , JHEP 04
Original
1912
Earlier work this paper cites.
N. Arkani-Hamed, T. Lam and M. Spradlin, Non-perturbative geometries for planar 𝒩 \mathcal{N} = 4 SYM amplitudes , JHEP 03
Original
1912
Earlier work this paper cites.
N. Henke and G. Papathanasiou, How tropical are seven- and eight-particle amplitudes? , JHEP 08
Original
1912
Earlier work this paper cites.
O. Steinmann, Über den zusammenhang zwischen den wightmanfunktionen und den retardierten kommutatoren , Helvetica Physica Acta 33
1960
Earlier work this paper cites.
O. Steinmann, Wightman-funktionen und retardierte kommutatoren. ii , Helvetica Physica Acta 33
1960
Earlier work this paper cites.
K.-T. Chen, Iterated path integrals , Bull. Am. Math. Soc. 83
1977
Earlier work this paper cites.
C. Anastasiou, Z. Bern, L.J. Dixon and D.A. Kosower, Planar amplitudes in maximally supersymmetric Yang-Mills theory , Phys. Rev. Lett. 91
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.
A.B. Goncharov, Galois symmetries of fundamental groupoids and noncommutative geometry , Duke Math. J. 128
2005
Earlier work this paper cites.
A.B. Goncharov et al., Galois symmetries of fundamental groupoids and noncommutative geometry , Duke Mathematical Journal 128
2005
Earlier work this paper cites.
J.S. Scott, Grassmannians and cluster algebras , Proceedings of the London Mathematical Society 92
2006
Earlier work this paper cites.
J.M. Drummond, J. Henn, V.A. Smirnov and E. Sokatchev, Magic identities for conformal four-point integrals , JHEP 01
2007
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.
S. He, Z. Li and C. Zhang, The symbol and alphabet of two-loop NMHV amplitudes from Q ¯ \bar{Q} equations , JHEP 03
Original
2009
Earlier work this paper cites.
J.M. Drummond, J.M. Henn and J. Plefka, Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory , JHEP 05
Original
2009
Earlier work this paper cites.
L.J. Mason and D. Skinner, Dual Superconformal Invariance, Momentum Twistors and Grassmannians , JHEP 11
Original
2009
Earlier work this paper cites.
F. Brown, Multiple zeta values and periods of moduli spaces 𝔪 ¯ 0 , n \overline{\mathfrak{m}}_{0,n} , in Annales scientifiques de l’École Normale Supérieure , vol. 42, pp. 371–489, 2009
2009
Earlier work this paper cites.