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

Abstract

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. For certain reasonable choices of basis at two and three loops the two constraints in unison appear strong enough to determine MHV integrands uniquely for all n.

27 pages, 14 figures; v2: very minor changes

References in corpus (10)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Notes on the scattering amplitude / Wilson loop duality
• Loops and trees
• On BCFW shifts of integrands and integrals
• Simple loop integrals and amplitudes in N=4 SYM
• Eliminating spurious poles from gauge-theoretic amplitudes
• On the structure of scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity

Cited by in corpus (7)

• Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps
• Generating All Tree Amplitudes in N=4 SYM by Inverse Soft Limit
• Perturbative correlation functions of null Wilson loops and local operators
• The two-loop six-point amplitude in ABJM theory
• Dual-Conformal Regularization of Infrared Loop Divergences and the Chiral Box Expansion
• Soft and Collinear Limits in $\mathcal{N}=8$ Supergravity using Double Copy Formalism
• Local integrands for the five-point amplitude in planar N=4 SYM up to five loops