Abstract
We present an explicit analytic calculation of the differential of the planar n-particle, two-loop MHV scattering amplitude in \( \mathcal{N}=4 \) super Yang-Mills theory. The result is expressed only in terms of the polylogarithm functions Li k (−x), for k = 1, 2, 3, with arguments x belonging to the special class of dual conformal cross-ratios known as cluster \( \mathcal{X} \)-coordinates. The surprising fact that these amplitudes may be expressed in this way provides a striking example of the manner in which the cluster structure on the kinematic configuration space underlies the structure of amplitudes in SYM theory.
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ArXiv ePrint: 1306.1833
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Golden, J., Spradlin, M. The differential of all two-loop MHV amplitudes in \( \mathcal{N}=4 \) Yang-Mills theory. J. High Energ. Phys. 2013, 111 (2013). https://doi.org/10.1007/JHEP09(2013)111
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DOI: https://doi.org/10.1007/JHEP09(2013)111