Two-Loop Amplitudes of Gluons and Octa-Cuts in N=4 Super Yang-Mills

Details Two-Loop Amplitudes of Gluons and Octa-Cuts in N=4 Super Yang-Mills Two-Loop Amplitudes of Gluons and Octa-Cuts in N=4 Super Yang-Mills

2005-06-15

arxiv.org/abs/hep-th/0506126v2

JHEP 0511 (2005) 036

Physics

High Energy Physics

High Energy Physics - Theory

38 pages, 23 figures, harvmac; minor corrections, references added

Scientific paper

10.1088/1126-6708/2005/11/036

After reduction techniques, two-loop amplitudes in N=4 super Yang-Mills theory can be written in a basis of integrals containing scalar double-box integrals with rational coefficients, though the complete basis is unknown. Generically, at two loops, the leading singular behavior of a scalar double box integral with seven propagators is captured by a hepta-cut. However, it turns out that a certain class of such integrals has an additional propagator-like singularity. One can then formally cut the new propagator to obtain an octa-cut which localizes the cut integral just as a quadruple cut does at one-loop. This immediately gives the coefficient of the scalar double box integral as a product of six tree-level amplitudes. We compute, as examples, several coefficients of the five- and six-gluon non-MHV two-loop amplitudes. We also discuss possible generalizations to higher loops.

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