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Feynman Integrals and Scattering Amplitudes from Wilson Loops.

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Summary

This study computes symbols for double pentagon integrals in N=4 super-Yang-Mills theory. These symbols are crucial for understanding scattering amplitudes, particularly maximally and next-to-maximally helicity violating amplitudes.

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Area of Science:

  • High-energy physics
  • Quantum field theory
  • String theory

Background:

  • N=4 super-Yang-Mills theory is a key model in theoretical physics.
  • Scattering amplitudes describe particle interactions.
  • Feynman integrals and Wilson loops are essential computational tools.

Purpose of the Study:

  • To compute symbols of general double pentagon integrals.
  • To apply these symbols to understand scattering amplitudes in N=4 super-Yang-Mills theory.
  • To analyze maximally helicity violating (MHV) and next-to-MHV (NMHV) amplitudes.

Main Methods:

  • Exploiting duality between Feynman integrals and null polygonal Wilson loops.
  • Symbolic computation of multi-loop integrals.
  • Analysis of the structure of scattering amplitudes.

Main Results:

  • First-time computation of symbols for general double pentagon integrals.
  • Determination of the finite part of two-loop MHV amplitudes.
  • Calculation of finite components of NMHV amplitudes for all multiplicities.
  • Identification of 164 rational and 96 algebraic letters in the symbol structure.

Conclusions:

  • The computed symbols provide a new tool for studying scattering amplitudes.
  • The results offer insights into the structure of N=4 super-Yang-Mills theory.
  • The cancellation of algebraic letters in specific amplitude components simplifies their analysis.