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.
L. Brink, J. H. Schwarz and J. Scherk, Supersymmetric Yang-Mills Theories , Nucl. Phys. B121
1977
Earlier work this paper cites.
F. Gliozzi, J. Scherk and D. I. Olive, Supersymmetry, Supergravity Theories and the Dual Spinor Model , Nucl. Phys. B122
1977
Earlier work this paper cites.
N. I. Usyukina and A. I. Davydychev, Exact results for three and four point ladder diagrams with an arbitrary number of rungs , Phys. Lett. B305
1993
Earlier work this paper cites.
Z. Bern, J. S. Rozowsky and B. Yan, Two loop four gluon amplitudes in N=4 superYang-Mills , Phys. Lett. B401
1997
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar, M. Perelstein and J. S. Rozowsky, On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences , Nucl. Phys. B530
1998
Earlier work this paper cites.
E. Remiddi and J. Vermaseren, Harmonic polylogarithms , Int.J.Mod.Phys. A15
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. 43
2002
Earlier work this paper cites.
S. Weinzierl, Symbolic expansion of transcendental functions , Comput.Phys.Commun. 145
2002
Earlier work this paper cites.
A. P. Isaev, Multiloop Feynman integrals and conformal quantum mechanics , Nucl. Phys. B662
2003
Earlier work this paper cites.
F. C. Brown, Single-valued multiple polylogarithms in one variable , C. R. Acad. Sci. Paris, Ser. I 338
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. 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.
N. Arkani-Hamed and J. Trnka, The Amplituhedron , JHEP 1410
Original
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.
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.
Z. Bern, J. Carrasco, H. Johansson and D. Kosower, Maximally supersymmetric planar Yang-Mills amplitudes at five loops , Phys.Rev. D76
Original
2007
Earlier work this paper cites.
L. F. Alday and J. M. Maldacena, Gluon scattering amplitudes at strong coupling , JHEP 0706
Original
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.
Z. Bern, J. J. Carrasco, D. Forde, H. Ita and H. Johansson, Unexpected Cancellations in Gravity Theories , Phys. Rev. D77
Original
2008
Earlier work this paper cites.
J. Drummond, G. Korchemsky and E. Sokatchev, Conformal properties of four-gluon planar amplitudes and Wilson loops , Nucl.Phys. B795
Original
2008
Earlier work this paper cites.
D. Nguyen, M. Spradlin and A. Volovich, New Dual Conformally Invariant Off-Shell Integrals , Phys. Rev. D77
Original
2008
Earlier work this paper cites.
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
Earlier work this paper cites.
L. Mason and D. Skinner, Dual Superconformal Invariance, Momentum Twistors and Grassmannians , JHEP 0911
Original
2009
Earlier work this paper cites.
N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, A Duality for the S Matrix , JHEP 03
Original
2010
Earlier work this paper cites.
Z. Bern, J. J. M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory , Phys. Rev. Lett. 105
Original
2010
Earlier work this paper cites.
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
Earlier work this paper cites.
D. J. Broadhurst and A. I. Davydychev, Exponential suppression with four legs and an infinity of loops , Nucl. Phys. Proc. Suppl. 205-206
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.
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, S. Caron-Huot and J. Trnka, The All-Loop Integrand for Scattering Amplitudes in Planar N=4 SYM , JHEP 1101
Original
2011
Earlier work this paper cites.
N. Arkani-Hamed, J. Bourjaily, F. Cachazo and J. Trnka, Local Spacetime Physics from the Grassmannian , JHEP 01
Original
2011
Earlier work this paper cites.
J. J. M. Carrasco and H. Johansson, Generic multiloop methods and application to N=4 super-Yang-Mills , J. Phys. A44
Original
2011
Earlier work this paper cites.
J. Gluza, K. Kajda and D. A. Kosower, Towards a Basis for Planar Two-Loop Integrals , Phys. Rev. D83
Original
2011
Earlier work this paper cites.

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2018

The Double Pentaladder Integral to All Orders

Caron-Huot, Simon, Dixon, Lance J., von Hippel, Matt et al.

Understand

We compute dual-conformally invariant ladder integrals that are capped off by pentagons at each end of the ladder.

Such integrals appear in six-point amplitudes in planar N=4 super-Yang-Mills theory.
We provide exact, finite-coupling formulas for the basic double pentaladder integrals as a single Mellin integral over hypergeometric functions.
For particular choices of the dual conformal cross ratios, we can evaluate the integral at weak coupling to high loop orders in terms of multiple polylogarithms.

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.
L. Brink, J. H. Schwarz and J. Scherk, Supersymmetric Yang-Mills Theories , Nucl. Phys. B121
1977
Earlier work this paper cites.
F. Gliozzi, J. Scherk and D. I. Olive, Supersymmetry, Supergravity Theories and the Dual Spinor Model , Nucl. Phys. B122
1977
Earlier work this paper cites.
N. I. Usyukina and A. I. Davydychev, Exact results for three and four point ladder diagrams with an arbitrary number of rungs , Phys. Lett. B305
1993
Earlier work this paper cites.
Z. Bern, J. S. Rozowsky and B. Yan, Two loop four gluon amplitudes in N=4 superYang-Mills , Phys. Lett. B401
1997
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar, M. Perelstein and J. S. Rozowsky, On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences , Nucl. Phys. B530
1998
Earlier work this paper cites.
E. Remiddi and J. Vermaseren, Harmonic polylogarithms , Int.J.Mod.Phys. A15
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. 43
2002
Earlier work this paper cites.
S. Weinzierl, Symbolic expansion of transcendental functions , Comput.Phys.Commun. 145
2002
Earlier work this paper cites.
A. P. Isaev, Multiloop Feynman integrals and conformal quantum mechanics , Nucl. Phys. B662
2003
Earlier work this paper cites.
F. C. Brown, Single-valued multiple polylogarithms in one variable , C. R. Acad. Sci. Paris, Ser. I 338
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. 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.
N. Arkani-Hamed and J. Trnka, The Amplituhedron , JHEP 1410
Original
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.
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.
Z. Bern, J. Carrasco, H. Johansson and D. Kosower, Maximally supersymmetric planar Yang-Mills amplitudes at five loops , Phys.Rev. D76
Original
2007
Earlier work this paper cites.
L. F. Alday and J. M. Maldacena, Gluon scattering amplitudes at strong coupling , JHEP 0706
Original
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.
Z. Bern, J. J. Carrasco, D. Forde, H. Ita and H. Johansson, Unexpected Cancellations in Gravity Theories , Phys. Rev. D77
Original
2008
Earlier work this paper cites.
J. Drummond, G. Korchemsky and E. Sokatchev, Conformal properties of four-gluon planar amplitudes and Wilson loops , Nucl.Phys. B795
Original
2008
Earlier work this paper cites.
D. Nguyen, M. Spradlin and A. Volovich, New Dual Conformally Invariant Off-Shell Integrals , Phys. Rev. D77
Original
2008
Earlier work this paper cites.
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
Earlier work this paper cites.
L. Mason and D. Skinner, Dual Superconformal Invariance, Momentum Twistors and Grassmannians , JHEP 0911
Original
2009
Earlier work this paper cites.
N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, A Duality for the S Matrix , JHEP 03
Original
2010
Earlier work this paper cites.
Z. Bern, J. J. M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory , Phys. Rev. Lett. 105
Original
2010
Earlier work this paper cites.
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
Earlier work this paper cites.
D. J. Broadhurst and A. I. Davydychev, Exponential suppression with four legs and an infinity of loops , Nucl. Phys. Proc. Suppl. 205-206
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.
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, S. Caron-Huot and J. Trnka, The All-Loop Integrand for Scattering Amplitudes in Planar N=4 SYM , JHEP 1101
Original
2011
Earlier work this paper cites.
N. Arkani-Hamed, J. Bourjaily, F. Cachazo and J. Trnka, Local Spacetime Physics from the Grassmannian , JHEP 01
Original
2011
Earlier work this paper cites.
J. J. M. Carrasco and H. Johansson, Generic multiloop methods and application to N=4 super-Yang-Mills , J. Phys. A44
Original
2011
Earlier work this paper cites.
J. Gluza, K. Kajda and D. A. Kosower, Towards a Basis for Planar Two-Loop Integrals , Phys. Rev. D83
Original
2011
Earlier work this paper cites.