Complete four-loop four-point amplitude in N=4 super-Yang-Mills theory

By Z. Bern, J. J. Carrasco, L. Dixon, H. Johansson, R. Roiban. 2010

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We present the complete four-loop four-point amplitude in N = 4 super-Yang-Mills theory, for a general gauge group and general D-dimensional covariant kinematics, and including all non-planar contributions. We use the method of maximal cuts - an efficient application of the unitarity method - to construct the result in terms of 50 four-loop integrals. We give graphical rules, valid in D-dimensions, for obtaining various non-planar contributions from previously-determined terms. We examine the ultraviolet behavior of the amplitude near D = 11/2. The non-planar terms are as well-behaved in the ultraviolet as the planar terms. However, in the color decomposition of the three- and four-loop amplitude for an SU(N{sub c}) gauge group, the coefficients of the double-trace terms are better behaved in the ultraviolet than are the single-trace terms. The results from this paper were an important step toward obtaining the corresponding amplitude in N = 8 supergravity, which confirmed the existence of cancellations beyond those needed for ultraviolet finiteness at four loops in four dimensions. Evaluation of the loop integrals near D = 4 would permit tests of recent conjectures and results concerning the infrared behavior of four-dimensional massless gauge theory.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ec20a95f995f89b8a49109f7a3b74652a048895a

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In Nuclear and High Energy Physics

  1. R. Boels
  2. Gang Yang
  3. Bernd A. Kniehl
  4. O. Tarasov
  5. H. Johansson
  6. R. Monteiro
  7. Alexander Ochirov
  8. D. O’Connell

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