Analytic two-loop form factors in N=4 SYM

Abstract

We derive a compact expression for the three-point MHV form factors of half-BPS operators in N=4 super Yang-Mills at two loops. The main tools of our calculation are generalised unitarity applied at the form factor level, and the compact expressions for supersymmetric tree-level form factors and amplitudes entering the cuts. We confirm that infrared divergences exponentiate as expected, and that collinear factorisation is entirely captured by an ABDK/BDS ansatz. Next, we construct the two-loop remainder function obtained by subtracting this ansatz from the full two-loop form factor and compute it numerically. Using symbology, combined with various physical constraints and symmetries, we find a unique solution for its symbol. With this input we construct a remarkably compact analytic expression for the remainder function, which contains only classical polylogarithms, and compare it to our numerical results. Furthermore, we make the surprising observation that our remainder is equal to the maximally transcendental piece of a closely related two-loop amplitude in QCD.

34 pages, 6 figures. v2: typos fixed, references added. Relation to hexagon remainder discussed in new section 4.6

References in corpus (12)

• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for Amplitudes and Wilson Loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Hexagon Wilson loop = six-gluon MHV amplitude
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Form factors at strong coupling via a Y-system
• Two-Loop QCD Corrections to the Helicity Amplitudes for $H\to$ 3 partons
• AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals
• Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops
• On form factors in N=4 sym
• The three-loop form factor in N=4 super Yang-Mills
• Numerical Evaluation of Tensor Feynman Integrals in Euclidean Kinematics

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