From dlogs to dilogs; the super Yang-Mills MHV amplitude revisited

Abstract

Recently, loop integrands for certain Yang-Mills scattering amplitudes and correlation functions have been shown to be systematically expressible in dlog form, raising the possibility that these loop integrals can be performed directly without Feynman parameters. We do so here to give a new description of the planar 1-loop MHV amplitude in N = 4 super Yang-Mills theory. We explicitly incorporate the standard Feynman i epsilon prescription into the integrands. We find that the generic MHV diagram contributing to the 1-loop MHV amplitude, known as Kermit, is dual conformal invariant up to the choice of reference twistor explicit in our axial gauge (the generic MHV diagram was already known to be finite). The new formulae for the amplitude are nontrivially related to previous ones in the literature. The divergent diagrams are evaluated using mass regularization. Our techniques extend directly to higher loop diagrams, and we illustrate this by sketching the evaluation of a non-trivial 2-loop example. We expect this to lead to a simple and efficient method for computing amplitudes and correlation functions with less supersymmetry and without the assumption of planarity.

v2. minor changes and updated discussion of mass regularization

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• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• ABJM amplitudes and the positive orthogonal grassmannian
• The Double Pentaladder Integral to All Orders
• Spectral Parameters for Scattering Amplitudes in N=4 Super Yang-Mills Theory
• Landau Singularities from the Amplituhedron
• Multi-Loop Positivity of the Planar $\mathcal{N}=4$ SYM Six-Point Amplitude
• On-Shell Diagrams for N = 8 Supergravity Amplitudes
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory at multi-Regge kinematics: Conformal Regge pole contribution
• Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\mathcal{N}=4$ Super Yang-Mills and $\mathcal{N}=8$ Supergravity
• Manifestly Dual-Conformal Loop Integration
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• Twistor actions for gauge theory and gravity
• Worldsheet factorization for twistor-strings
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory in multi-Regge kinematics: Conformal Regge cut contribution
• The four-loop six-gluon NMHV ratio function
• Twistor fishnets
• $\mathcal{N}=7$ On-Shell Diagrams and Supergravity Amplitudes in Momentum Twistor Space
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes