期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 3, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP03(2012)032
关键词
Supersymmetric gauge theory; Scattering Amplitudes
资金
- Harvard Society of Fellows
- US Department of Energy [DE-FG02-91ER40654, DE-FG02-91ER40688, DE-FG02-11ER41742]
- National Science Foundation [PHY-0756966, PHY-0643150 PECASE]
- Sloan Research Foundation
Infrared divergences in scattering amplitudes arise when a loop momentum l becomes collinear with a massless external momentum p. In gauge theories, it is known that the L-loop logarithm of a planar amplitude has much softer infrared singularities than the L-loop amplitude itself. We argue that planar amplitudes in N = 4 super-Yang-Mills theory enjoy softer than expected behavior as l parallel to p already at the level of the integrand. Moreover, we conjecture that the four-point integrand can be uniquely determined, to any loop-order, by imposing the correct soft-behavior of the logarithm together with dual conformal invariance and dihedral symmetry. We use these simple criteria to determine explicit formulae for the four-point integrand through seven-loops, finding perfect agreement with previously known results through five-loops. As an input to this calculation, we enumerate all four-point dual conformally invariant (DCI) integrands through seven-loops, an analysis which is aided by several graph-theoretic theorems we prove about general DCI integrands at arbitrary loop-order. The six- and seven-loop amplitudes receive non-zero contributions from 229 and 1873 individual DCI diagrams respectively. PDF and MATHEMATICA files with all of our results are provided at http://goo.gl/qIKe8.
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