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2012

Collinear and Soft Limits of Multi-Loop Integrands in N=4 Yang-Mills

Golden, John, Spradlin, Marcus

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It has been argued in arXiv:1112.6432 that the planar four-point integrand in N=4 super Yang-Mills theory is uniquely determined by dual conformal invariance together with the absence of a double pole in the integrand of the logarithm in the limit as a loop integration variable becomes collinear with an external momentum.

In this paper we reformulate this condition in a simple way in terms of the amplitude itself, rather than its logarithm, and verify that it holds for two- and three-loop MHV integrands for n>4.
We investigate the extent to which this collinear constraint and a constraint on the soft behavior of integrands can be used to determine integrands.
We find an interesting complementarity whereby the soft constraint becomes stronger while the collinear constraint becomes weaker at larger n.

Collinear and Soft Limits of Multi-Loop Integrands in N=4 Yang-Mills · Around

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Similar

J. M. Drummond, J. Henn, G. P. Korchemsky and E. Sokatchev, “Dual superconformal symmetry of scattering amplitudes in 𝒩 = 4 \mathcal{N}=4 super-Yang-Mills theory,” Nucl. Phys. B 828
Original
2010
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V. Del Duca, C. Duhr and V. A. Smirnov, “An Analytic Result for the Two-Loop Hexagon Wilson Loop in 𝒩 = 4 \mathcal{N}=4 SYM,” JHEP 1003
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A. B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, Phys. Rev. Lett. 105
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2010
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S. Caron-Huot, “Loops and trees,” JHEP 1105
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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 \mathcal{N}=4 SYM,” JHEP 1101

Then

L. F. Alday, B. Eden, G. P. Korchemsky, J. Maldacena and E. Sokatchev, “From correlation functions to Wilson loops,” JHEP 1109
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2011
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B. Eden, G. P. Korchemsky and E. Sokatchev, “From correlation functions to scattering amplitudes,” JHEP 1112
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2011
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J. M. Drummond and J. M. Henn, “Simple loop integrals and amplitudes in 𝒩 = 4 \mathcal{N}=4 SYM,” JHEP 1105
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2011
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J. Gluza, K. Kajda and D. A. Kosower, “Towards a Basis for Planar Two-Loop Integrals,” Phys. Rev. D 83
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A. V. Belitsky, G. P. Korchemsky and E. Sokatchev, “Are scattering amplitudes dual to super Wilson loops?,” Nucl. Phys. B 855

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Original

2011

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S. Caron-Huot, “Notes on the scattering amplitude/Wilson loop duality,” JHEP 1107

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T. Adamo, M. Bullimore, L. Mason and D. Skinner, “Scattering Amplitudes and Wilson Loops in Twistor Space,” J. Phys. A 44

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F. Cachazo and D. Skinner, “On the structure of scattering amplitudes in 𝒩 = 4 \mathcal{N}=4 super Yang-Mills and 𝒩 = 8 \mathcal{N}=8 supergravity,” arXiv:0801.4574 [hep-th]

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B. Eden, P. Heslop, G. P. Korchemsky and E. Sokatchev, “The super-correlator/super-amplitude duality: Part I,” arXiv:1103.3714 [hep-th]

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B. Eden, P. Heslop, G. P. Korchemsky and E. Sokatchev, “The super-correlator/super-amplitude duality: Part II,” arXiv:1103.4353 [hep-th]

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B. Eden, P. Heslop, G. P. Korchemsky and E. Sokatchev, “Hidden symmetry of four-point correlation functions and amplitudes in 𝒩 = 4 \mathcal{N}=4 SYM,” arXiv:1108.3557 [hep-th]

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L. J. Dixon, J. M. Drummond and J. M. Henn, “Analytic result for the two-loop six-point NMHV amplitude in 𝒩 = 4 \mathcal{N}=4 super Yang-Mills theory,” JHEP 1201

2012

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