Built on

J. Golden, A. J. McLeod, M. Spradlin and A. Volovich, The Sklyanin Bracket and Cluster Adjacency at All Multiplicity , JHEP 03
Original
1902
Earlier work this paper cites.
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.
C. Duhr and F. Dulat, PolyLogTools — polylogs for the masses , JHEP 08
Original
1904
Earlier work this paper cites.
J. Elias Miró, A. L. Guerrieri, A. Hebbar, J. Penedones and P. Vieira, Flux Tube S-matrix Bootstrap , Phys. Rev. Lett. 123
Original
1906
Earlier work this paper cites.
S. Caron-Huot, L. J. Dixon, F. Dulat, M. Von Hippel, A. J. McLeod and G. Papathanasiou, The Cosmic Galois Group and Extended Steinmann Relations for Planar 𝒩 = 4 \mathcal{N}=4 SYM Amplitudes , JHEP 09
Original
1906
Earlier work this paper cites.
J. Drummond, J. Foster, Ö. Gürdoğan and C. Kalousios, Tropical Grassmannians, cluster algebras and scattering amplitudes , JHEP 04
Original
1907
Earlier work this paper cites.
L. Córdova, Y. He, M. Kruczenski and P. Vieira, The O(N) S-matrix Monolith , JHEP 04
Original
1909
Earlier work this paper cites.
C. Bercini, M. Fabri, A. Homrich and P. Vieira, S-matrix bootstrap: Supersymmetry, Z 2 Z_{2} , and Z 4 Z_{4} symmetry , Phys. Rev. D 101
Original
1909
Earlier work this paper cites.
J. Drummond, J. Foster, Ö. Gürdoğan and C. Kalousios, Algebraic singularities of scattering amplitudes from tropical geometry , 1912.08217
Original
1912
Earlier work this paper cites.
N. Arkani-Hamed, T. Lam and M. Spradlin, Non-perturbative geometries for planar 𝒩 = 4 \mathcal{N}=4 SYM amplitudes , 1912.08222
Original
1912
Earlier work this paper cites.
N. Henke and G. Papathanasiou, How tropical are seven- and eight-particle amplitudes? , 1912.08254
Original
1912
Earlier work this paper cites.
J. L. Bourjaily, M. Volk and M. Von Hippel, Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder , JHEP 02
Original
1912
Earlier work this paper cites.
V. Del Duca, S. Druc, J. Drummond, C. Duhr, F. Dulat, R. Marzucca et al., All-order amplitudes at any multiplicity in the multi-Regge limit , Phys. Rev. Lett. 124
Original
1912
Earlier work this paper cites.
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.
R. J. Eden, P. V. Landshoff, D. I. Olive and J. C. Polkinghorne, The Analytic S-Matrix . Cambridge University Press, 1966
1966
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. B 425
1994
Earlier work this paper cites.
E. Remiddi and J. Vermaseren, Harmonic polylogarithms , Int. J. Mod. Phys. A 15
2000
Earlier work this paper cites.
B. Basso, L. J. Dixon and G. Papathanasiou, The Origin of the Six-Gluon Amplitude in Planar 𝒩 = 4 \mathcal{N}=4 SYM , Phys. Rev. Lett. 124
Original
2001
Earlier work this paper cites.
J. Drummond, J. Foster, Ö. Gürdoğan and C. Kalousios, Tropical fans, scattering equations and amplitudes , 2002.04624
Original
2002
Earlier work this paper cites.
S. Caron-Huot, L. J. Dixon, J. M. Drummond, F. Dulat, J. Foster, Ö. Gürdoğan et al., The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes , in 19th Hellenic School and Workshops on Elementary Particle Physics and Gravity , 5, 2020, 2005.06735
Original
2005
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.
Ö. Gürdoğan and M. Parisi, Cluster patterns in Landau and Leading Singularities via the Amplituhedron , 2005.07154
Original
2005
Earlier work this paper cites.
J. Mago, A. Schreiber, M. Spradlin and A. Volovich, A Note on One-loop Cluster Adjacency in N = 4 SYM , 2005.07177
Original
2005
Earlier work this paper cites.
J. Bartels, Analytic structure of the 8-point scattering amplitude in multi-Regge kinematics in N N =4 SYM : conformal Regge pole and Regge cut contributions , 2005.08818
Original
2005
Earlier work this paper cites.
F. Brown and C. Duhr, A double integral of dlog forms which is not polylogarithmic , 2006.09413
Original
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.
Z. Bern, M. Czakon, L. J. Dixon, D. A. Kosower and V. A. Smirnov, The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory , Phys. Rev. D75
2007
Earlier work this paper cites.

Similar

Z. Bern, J. Carrasco, H. Johansson and D. Kosower, Maximally supersymmetric planar Yang-Mills amplitudes at five loops , Phys.Rev. D76
Original
2007
Cited alongside, same era.
L. F. Alday and J. M. Maldacena, Gluon scattering amplitudes at strong coupling , JHEP 06
Original
2007
Cited alongside, same era.
L. F. Alday and J. Maldacena, Comments on gluon scattering amplitudes via AdS/CFT , JHEP 0711
Original
2007
Cited alongside, same era.
N. Beisert, B. Eden and M. Staudacher, Transcendentality and Crossing , J. Stat. Mech. 0701
2007
Cited alongside, same era.
J. Drummond, J. Henn, G. Korchemsky and E. Sokatchev, The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude , Phys.Lett. B662
Original

Then

B. Basso, A. Sever and P. Vieira, Spacetime and Flux Tube S-Matrices at Finite Coupling for N=4 Supersymmetric Yang-Mills Theory , Phys. Rev. Lett. 111
Original
2013
Later among the works it cites.
L. J. Dixon and M. von Hippel, Bootstrapping an NMHV amplitude through three loops , JHEP 1410
Original
2014
Later among the works it cites.
J. Golden, A. B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, Motivic Amplitudes and Cluster Coordinates , JHEP 1401
Original
2014
Later among the works it cites.
L. J. Dixon, J. M. Drummond, C. Duhr and J. Pennington, The four-loop remainder function and multi-Regge behavior at NNLLA in planar 𝒩 = 4 \mathcal{N}=4 super-Yang-Mills theory , JHEP 1406
Original
2014
Later among the works it cites.
O. Schnetz, Graphical functions and single-valued multiple polylogarithms , Commun. Num. Theor. Phys. 08

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2020

Lifting Heptagon Symbols to Functions

Dixon, Lance J., Liu, Yu-Ting

Understand

Seven-point amplitudes in planar ${\cal N}=4$ super-Yang-Mills theory have previously been constructed through four loops using the Steinmann cluster bootstrap, but only at the level of the symbol.

We promote these symbols to actual functions, by specifying their first derivatives and boundary conditions on a particular two-dimensional surface.
To do this, we impose branch-cut conditions and construct the entire heptagon function space through weight six.
We plot the amplitudes on a few lines in the bulk Euclidean region, and explore the properties of the heptagon function space under the coaction associated with multiple polylogarithms.

Built on

J. Golden, A. J. McLeod, M. Spradlin and A. Volovich, The Sklyanin Bracket and Cluster Adjacency at All Multiplicity , JHEP 03
Original
1902
Earlier work this paper cites.
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.
C. Duhr and F. Dulat, PolyLogTools — polylogs for the masses , JHEP 08
Original
1904
Earlier work this paper cites.
J. Elias Miró, A. L. Guerrieri, A. Hebbar, J. Penedones and P. Vieira, Flux Tube S-matrix Bootstrap , Phys. Rev. Lett. 123
Original
1906
Earlier work this paper cites.
S. Caron-Huot, L. J. Dixon, F. Dulat, M. Von Hippel, A. J. McLeod and G. Papathanasiou, The Cosmic Galois Group and Extended Steinmann Relations for Planar 𝒩 = 4 \mathcal{N}=4 SYM Amplitudes , JHEP 09
Original
1906
Earlier work this paper cites.
J. Drummond, J. Foster, Ö. Gürdoğan and C. Kalousios, Tropical Grassmannians, cluster algebras and scattering amplitudes , JHEP 04
Original
1907
Earlier work this paper cites.
L. Córdova, Y. He, M. Kruczenski and P. Vieira, The O(N) S-matrix Monolith , JHEP 04
Original
1909
Earlier work this paper cites.
C. Bercini, M. Fabri, A. Homrich and P. Vieira, S-matrix bootstrap: Supersymmetry, Z 2 Z_{2} , and Z 4 Z_{4} symmetry , Phys. Rev. D 101
Original
1909
Earlier work this paper cites.
J. Drummond, J. Foster, Ö. Gürdoğan and C. Kalousios, Algebraic singularities of scattering amplitudes from tropical geometry , 1912.08217
Original
1912
Earlier work this paper cites.
N. Arkani-Hamed, T. Lam and M. Spradlin, Non-perturbative geometries for planar 𝒩 = 4 \mathcal{N}=4 SYM amplitudes , 1912.08222
Original
1912
Earlier work this paper cites.
N. Henke and G. Papathanasiou, How tropical are seven- and eight-particle amplitudes? , 1912.08254
Original
1912
Earlier work this paper cites.
J. L. Bourjaily, M. Volk and M. Von Hippel, Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder , JHEP 02
Original
1912
Earlier work this paper cites.
V. Del Duca, S. Druc, J. Drummond, C. Duhr, F. Dulat, R. Marzucca et al., All-order amplitudes at any multiplicity in the multi-Regge limit , Phys. Rev. Lett. 124
Original
1912
Earlier work this paper cites.
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.
R. J. Eden, P. V. Landshoff, D. I. Olive and J. C. Polkinghorne, The Analytic S-Matrix . Cambridge University Press, 1966
1966
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. B 425
1994
Earlier work this paper cites.
E. Remiddi and J. Vermaseren, Harmonic polylogarithms , Int. J. Mod. Phys. A 15
2000
Earlier work this paper cites.
B. Basso, L. J. Dixon and G. Papathanasiou, The Origin of the Six-Gluon Amplitude in Planar 𝒩 = 4 \mathcal{N}=4 SYM , Phys. Rev. Lett. 124
Original
2001
Earlier work this paper cites.
J. Drummond, J. Foster, Ö. Gürdoğan and C. Kalousios, Tropical fans, scattering equations and amplitudes , 2002.04624
Original
2002
Earlier work this paper cites.
S. Caron-Huot, L. J. Dixon, J. M. Drummond, F. Dulat, J. Foster, Ö. Gürdoğan et al., The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes , in 19th Hellenic School and Workshops on Elementary Particle Physics and Gravity , 5, 2020, 2005.06735
Original
2005
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.
Ö. Gürdoğan and M. Parisi, Cluster patterns in Landau and Leading Singularities via the Amplituhedron , 2005.07154
Original
2005
Earlier work this paper cites.
J. Mago, A. Schreiber, M. Spradlin and A. Volovich, A Note on One-loop Cluster Adjacency in N = 4 SYM , 2005.07177
Original
2005
Earlier work this paper cites.
J. Bartels, Analytic structure of the 8-point scattering amplitude in multi-Regge kinematics in N N =4 SYM : conformal Regge pole and Regge cut contributions , 2005.08818
Original
2005
Earlier work this paper cites.
F. Brown and C. Duhr, A double integral of dlog forms which is not polylogarithmic , 2006.09413
Original
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.
Z. Bern, M. Czakon, L. J. Dixon, D. A. Kosower and V. A. Smirnov, The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory , Phys. Rev. D75
2007
Earlier work this paper cites.

Similar

Z. Bern, J. Carrasco, H. Johansson and D. Kosower, Maximally supersymmetric planar Yang-Mills amplitudes at five loops , Phys.Rev. D76
Original
2007
Cited alongside, same era.
L. F. Alday and J. M. Maldacena, Gluon scattering amplitudes at strong coupling , JHEP 06
Original
2007
Cited alongside, same era.
L. F. Alday and J. Maldacena, Comments on gluon scattering amplitudes via AdS/CFT , JHEP 0711
Original
2007
Cited alongside, same era.
N. Beisert, B. Eden and M. Staudacher, Transcendentality and Crossing , J. Stat. Mech. 0701
2007
Cited alongside, same era.
J. Drummond, J. Henn, G. Korchemsky and E. Sokatchev, The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude , Phys.Lett. B662
Original

Then

B. Basso, A. Sever and P. Vieira, Spacetime and Flux Tube S-Matrices at Finite Coupling for N=4 Supersymmetric Yang-Mills Theory , Phys. Rev. Lett. 111
Original
2013
Later among the works it cites.
L. J. Dixon and M. von Hippel, Bootstrapping an NMHV amplitude through three loops , JHEP 1410
Original
2014
Later among the works it cites.
J. Golden, A. B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, Motivic Amplitudes and Cluster Coordinates , JHEP 1401
Original
2014
Later among the works it cites.
L. J. Dixon, J. M. Drummond, C. Duhr and J. Pennington, The four-loop remainder function and multi-Regge behavior at NNLLA in planar 𝒩 = 4 \mathcal{N}=4 super-Yang-Mills theory , JHEP 1406
Original
2014
Later among the works it cites.
O. Schnetz, Graphical functions and single-valued multiple polylogarithms , Commun. Num. Theor. Phys. 08

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2008

Cited alongside, same era.

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

Cited alongside, same era.

J. Drummond, J. Henn, G. Korchemsky and E. Sokatchev, Hexagon Wilson loop = six-gluon MHV amplitude , Nucl.Phys. B815

Original

2009

Cited alongside, same era.

F. C. Brown, Multiple zeta values and periods of moduli spaces 𝔐 ¯ 0 , n ( ℝ ) \overline{\mathfrak{M}}_{0,n}(\mathbb{R}) , Annales Sci.Ecole Norm.Sup. 42

2009

Cited alongside, same era.

L. Mason and D. Skinner, Dual Superconformal Invariance, Momentum Twistors and Grassmannians , JHEP 0911

Original

2009

Cited alongside, same era.

F. Brown, The Massless higher-loop two-point function , Commun. Math. Phys. 287

Original

2009

Cited alongside, same era.

J. Drummond, J. Henn, G. Korchemsky and E. Sokatchev, Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes , Nucl.Phys. B826

Original