2017/09/18 by Zvi Bern, Michael Enciso, H. Ita +2
Mathematics · Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Conformal map #Conformal symmetry #Crossing #Differential equation #Feynman diagram #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #Physics #Planar #Propagator #Quantum mechanics #Scattering amplitude #Unitarity #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.96.096017
published as Phys. Rev. D 96, 096017 (2017) · 66 pages, 14 figures, REVTeX
arxiv created 2017/09/18 · openalex publication_date 2017/11/21 · arxiv updated 2017/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that dual conformal symmetry, mainly studied in planar N=4 super-Yang-Mills theory, has interesting consequences for Feynman integrals in nonsupersymmetric theories such as QCD, including the nonplanar sector. A simple observation is that dual conformal transformations preserve unitarity cut conditions for any planar integrals, including those without dual conformal symmetry. Such transformations generate differential equations without raised propagator powers, often with the right-hand side of the system proportional to the dimensional regularization parameter \ensuremathε. A nontrivial subgroup of dual conformal transformations, which leaves all external momenta invariant, generates integration-by-parts relations without raised propagator powers, reproducing, in a simpler form, previous results from computational algebraic geometry for several examples with up to two loops and five legs. By opening up the two-loop three- and four-point nonplanar diagrams into planar ones, we find a nonplanar analog of dual conformal symmetry. As for the planar case, this is used to generate integration-by-parts relations and differential equations. This implies that the symmetry is tied to the analytic properties of the nonplanar sector of the two-loop four-point amplitude of N=4 super-Yang-Mills theory.