Built on

A. Belitsky, “A note on two-loop superloop,” Phys.Lett
Original
1924
Earlier work this paper cites.
V. Tarasov, L. Takhtajan, and L. Faddeev, “Local Hamiltonians for integrable quantum models on a lattice,” Theor.Math.Phys
1983
Earlier work this paper cites.
M. Gunaydin and N. Marcus, “The Spectrum of the s**5 Compactification of the Chiral N=2, D=10 Supergravity and the Unitary Supermultiplets of U(2, 2/4),” Class.Quant.Grav
1985
Earlier work this paper cites.
J. Blumlein and S. Kurth, “Harmonic sums and Mellin transforms up to two loop order,” Phys.Rev
1999
Earlier work this paper cites.
E. Remiddi and J. Vermaseren, “Harmonic polylogarithms,” Int.J.Mod.Phys
2000
Earlier work this paper cites.
S. Moch, P. Uwer, and S. Weinzierl, “Nested sums, expansion of transcendental functions and multiscale multiloop integrals,” J.Math.Phys
2002
Earlier work this paper cites.
V. Braun, G. Korchemsky, and D. Mueller, “The Uses of conformal symmetry in QCD,” Prog.Part.Nucl.Phys
2003
Earlier work this paper cites.
N. Beisert, “The complete one loop dilatation operator of N=4 superYang-Mills theory,” Nucl.Phys
2004
Earlier work this paper cites.
J. Blumlein, “Algebraic relations between harmonic sums and associated quantities,” Comput.Phys.Commun
2004
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
2005
Earlier work this paper cites.
B. Eden and M. Staudacher, “Integrability and transcendentality,” J.Stat.Mech
2006
Earlier work this paper cites.
D. Maitre, “HPL, a mathematica implementation of the harmonic polylogarithms,” Comput.Phys.Commun
2006
Earlier work this paper cites.
L. F. Alday and J. M. Maldacena, “Gluon scattering amplitudes at strong coupling,” JHEP
Original
2007
Earlier work this paper cites.
J. Drummond, J. Henn, V. Smirnov, and E. Sokatchev, “Magic identities for conformal four-point integrals,” JHEP
2007
Earlier work this paper cites.
G. Korchemsky, J. Drummond, and E. Sokatchev, “Conformal properties of four-gluon planar amplitudes and Wilson loops,” Nucl.Phys
Original
2008
Earlier work this paper cites.
A. Brandhuber, P. Heslop, and G. Travaglini, “MHV amplitudes in N=4 super Yang-Mills and Wilson loops,” Nucl.Phys
Original
2008
Earlier work this paper cites.
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
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 SYM,” JHEP
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
Original
2010
Earlier work this paper cites.

Similar

J. Drummond, J. Henn, G. Korchemsky, and E. Sokatchev, “Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory,” Nucl.Phys
Original
2010
Cited alongside, same era.
L. Mason and D. Skinner, “The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space,” JHEP
Original
2010
Cited alongside, same era.
L. Lipatov and A. Prygarin, “BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills,” Phys.Rev
Original
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Cited alongside, same era.
L. F. Alday, D. Gaiotto, J. Maldacena, A. Sever, and P. Vieira, “An Operator Product Expansion for Polygonal null Wilson Loops,” JHEP
Original
2011
Cited alongside, same era.
L. J. Dixon, J. M. Drummond, and J. M. Henn, “Bootstrapping the three-loop hexagon,” JHEP

Then

B. Eden, G. P. Korchemsky, and E. Sokatchev, “More on the duality correlators/amplitudes,” Phys.Lett
Original
2012
Later among the works it cites.
A. Belitsky, G. Korchemsky, and E. Sokatchev, “Are scattering amplitudes dual to super Wilson loops?,” Nucl.Phys
Original
2012
Later among the works it cites.
L. Freyhult, “Review of AdS/CFT Integrability, Chapter III.4: Twist States and the cusp Anomalous Dimension,” Lett.Math.Phys
Original
2012
Later among the works it cites.
L. J. Dixon, C. Duhr, and J. Pennington, “Single-valued harmonic polylogarithms and the multi-Regge limit,” JHEP
Original
2012
Later among the works it cites.
D. Maitre, “Extension of HPL to complex arguments,” Comput.Phys.Commun
2012

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2013

Hexagon Wilson Loop OPE and Harmonic Polylogarithms

Papathanasiou, Georgios

Understand

A recent, integrability-based conjecture in the framework of the Wilson loop OPE for N=4 SYM theory, predicts the leading OPE contribution for the hexagon MHV remainder function and NMHV ratio function to all loops, in integral form.

We prove that these integrals evaluate to a particular basis of harmonic polylogarithms, at any order in the weak coupling expansion.
The proof constitutes an algorithm for the direct computation of the integrals, which we employ in order to obtain the full (N)MHV OPE contribution in question up to 6 loops, and certain parts of it up to 12 loops.
We attach computer-readable files with our results, as well as an algorithm implementation which may be readily used to generate higher-loop corrections.

Built on

A. Belitsky, “A note on two-loop superloop,” Phys.Lett
Original
1924
Earlier work this paper cites.
V. Tarasov, L. Takhtajan, and L. Faddeev, “Local Hamiltonians for integrable quantum models on a lattice,” Theor.Math.Phys
1983
Earlier work this paper cites.
M. Gunaydin and N. Marcus, “The Spectrum of the s**5 Compactification of the Chiral N=2, D=10 Supergravity and the Unitary Supermultiplets of U(2, 2/4),” Class.Quant.Grav
1985
Earlier work this paper cites.
J. Blumlein and S. Kurth, “Harmonic sums and Mellin transforms up to two loop order,” Phys.Rev
1999
Earlier work this paper cites.
E. Remiddi and J. Vermaseren, “Harmonic polylogarithms,” Int.J.Mod.Phys
2000
Earlier work this paper cites.
S. Moch, P. Uwer, and S. Weinzierl, “Nested sums, expansion of transcendental functions and multiscale multiloop integrals,” J.Math.Phys
2002
Earlier work this paper cites.
V. Braun, G. Korchemsky, and D. Mueller, “The Uses of conformal symmetry in QCD,” Prog.Part.Nucl.Phys
2003
Earlier work this paper cites.
N. Beisert, “The complete one loop dilatation operator of N=4 superYang-Mills theory,” Nucl.Phys
2004
Earlier work this paper cites.
J. Blumlein, “Algebraic relations between harmonic sums and associated quantities,” Comput.Phys.Commun
2004
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
2005
Earlier work this paper cites.
B. Eden and M. Staudacher, “Integrability and transcendentality,” J.Stat.Mech
2006
Earlier work this paper cites.
D. Maitre, “HPL, a mathematica implementation of the harmonic polylogarithms,” Comput.Phys.Commun
2006
Earlier work this paper cites.
L. F. Alday and J. M. Maldacena, “Gluon scattering amplitudes at strong coupling,” JHEP
Original
2007
Earlier work this paper cites.
J. Drummond, J. Henn, V. Smirnov, and E. Sokatchev, “Magic identities for conformal four-point integrals,” JHEP
2007
Earlier work this paper cites.
G. Korchemsky, J. Drummond, and E. Sokatchev, “Conformal properties of four-gluon planar amplitudes and Wilson loops,” Nucl.Phys
Original
2008
Earlier work this paper cites.
A. Brandhuber, P. Heslop, and G. Travaglini, “MHV amplitudes in N=4 super Yang-Mills and Wilson loops,” Nucl.Phys
Original
2008
Earlier work this paper cites.
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
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 SYM,” JHEP
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
Original
2010
Earlier work this paper cites.