Hidden Beauty in Multiloop Amplitudes

Abstract

Planar L-loop maximally helicity violating amplitudes in N = 4 supersymmetric Yang-Mills theory are believed to possess the remarkable property of satisfying iteration relations in L. We propose a simple new method for studying the iteration relations for four-particle amplitudes which involves the use of certain linear differential operators and eliminates the need to fully evaluate any loop integrals. We carry out this procedure in explicit detail for the two-loop amplitude and argue that this method can be used to prove the iteration relations to all loops up to polynomials in logarithms.

21 pages, harvmac; v2: minor changes

Cited by in corpus (8)

• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Four-Loop Cusp Anomalous Dimension From Obstructions
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• New Dual Conformally Invariant Off-Shell Integrals
• Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory
• The two-loop vector form factor in the Sudakov limit
• Scattering amplitudes in strongly coupled N=4 SYM from semiclassical strings in AdS