Analytic two-loop form factors in \( \mathcal{N} = 4 \) SYM

  • Andreas Brandhuber
  • Gabriele Travaglini
  • Gang Yang


We derive a compact expression for the three-point MHV form factors of half- BPS operators in \( \mathcal{N} = 4 \) 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 symme- tries, 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 poly- logarithms, and compare it to our numerical results. Furthermore, we make the surprising observation that our remainder is equal to the maximally transcendental piece of the two- loop Higgs plus three-gluon scattering amplitudes in QCD.


Supersymmetric gauge theory Scattering Amplitudes QCD 


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Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Andreas Brandhuber
    • 1
    • 2
  • Gabriele Travaglini
    • 1
  • Gang Yang
    • 3
  1. 1.Centre for Research in String Theory, School of Physics and AstronomyQueen Mary University of LondonLondonUnited Kingdom
  2. 2.Department of Particle Physics and AstrophysicsWeizmann Institute of ScienceRehovotIsrael
  3. 3.II. Institut fu¨r Theoretische PhysikUniversita¨t HamburgHamburgGermany

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