Abstract
We present a formulation of the maximally supersymmetric \( \mathcal{N} \) = 4 gauge theory in Lorentz harmonic chiral (LHC) superspace. It is closely related to the twistor formulation of the theory but employs the simpler notion of Lorentz harmonic variables. They parametrize a two-sphere and allow us to handle efficiently infinite towers of higher-spin auxiliary fields defined on ordinary space-time. In this approach the chiral half of \( \mathcal{N} \) =4 supersymmetry is manifest. The other half is realized non-linearly and the algebra closes on shell. We give a straightforward derivation of the Feynman rules in coordinate space. We show that the LHC formulation of the \( \mathcal{N} \) = 4 super-Yang-Mills theory is remarkably similar to the harmonic superspace formulation of the \( \mathcal{N} \) = 2 gauge and hypermultiplet matter theories. In the twin paper arXiv:1601.06804 we apply the LHC formalism to the study of the non-chiral multipoint correlation functions of the \( \mathcal{N} \) = 4 stress-tensor supermultiplet.
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ArXiv ePrint: 1601.06803
Dedicated to the memory of Boris Zupnik, a colleague and a friend
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Chicherin, D., Sokatchev, E. \( \mathcal{N} \) = 4 super-Yang-Mills in LHC superspace part I: classical and quantum theory. J. High Energ. Phys. 2017, 62 (2017). https://doi.org/10.1007/JHEP02(2017)062
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DOI: https://doi.org/10.1007/JHEP02(2017)062