Two-loop iteration of five-point N=4 super-Yang-Mills amplitudes

Area of Science:

• High-energy physics
• Quantum field theory
• Supersymmetric gauge theories

Background:

• Planar maximally supersymmetric N=4 Yang-Mills theory is a crucial model in quantum field theory.
• Understanding its properties, particularly scattering amplitudes, is essential for theoretical advancements.
• A conjectured all-orders iteration relation for these amplitudes remained unproven in nontrivial cases.

Purpose of the Study:

• To explicitly compute and verify the conjectured all-orders iteration of planar maximally supersymmetric N=4 Yang-Mills theory.
• To investigate the nontrivial case of five-point two-loop amplitudes.
• To provide further evidence for the solvability of N=4 gauge theory.

Main Methods:

• Computation of required unitarity cuts of the integrand.
• Numerical evaluation of resulting integrals using a Mellin-Barnes representation.
• Utilizing the automated package developed by Czakon (Comput. Phys. Commun. 175, 559 (2006)).

Main Results:

• Explicit confirmation of the conjectured all-orders iteration relation for five-point two-loop amplitudes.
• Successful numerical evaluation of complex integrals, validating theoretical predictions.
• Demonstration of the iteration's validity in a nontrivial scenario.

Conclusions:

• The study provides concrete computational evidence supporting the iteration relation.
• This confirmation strengthens the hypothesis that N=4 Yang-Mills theory is a solvable model.
• The findings pave the way for further investigations into the exact solutions of supersymmetric gauge theories.