Systematics of One-Loop Scattering Amplitudes in N=4 Super Yang-Mills Theories

TL;DR

This paper analyzes one-loop scattering amplitudes in N=4 super Yang-Mills theories, revealing a limited set of integrals and relations between different amplitude types, supporting the maximal helicity violating paradigm.

Contribution

It demonstrates that the number of independent loop integrals is limited and confirms the relations between leading and sub-leading amplitudes, supporting the MHV diagram paradigm.

Findings

Limited number of independent integrals for n-particle processes.

Relations between A_{n;1} and A_{n;c} match conventional calculations.

Supports the maximal helicity violating diagram paradigm.

Abstract

One-loop scattering amplitudes in N=4 super Yang-Mills (SYM) theories are analyzed in the paradigm of maximal helicity violating Feynman diagrams. There are very limited number of loop integrals to be evaluated. For a process with n external particles, there are only [n/2]-1 generically independent integrals. Furthermore, the relations between leading N_c amplitudes A_{n;1} and sub-leading amplitudes A_{n;c} are found to be identical to those obtained from conventional field theory calculations, which can be interpreted as an indirect support for the paradigm.