Abstract
We localize the four-dimensional \( \mathcal{N}=4 \) super Yang-Mills theory on S 4 to the two-dimensional constrained Hitchin/Higgs-Yang-Mills (cHYM) theory on S 2. We show that expectation values of certain 1/8 BPS supersymmetric Wilson loops on S 2 in the 4d \( \mathcal{N}=4 \) SYMiscapturedbythe2dcHYMtheory. Wefurtherarguethatexpectationvalues of Wilson loops in the cHYM theory agree with the prescription “two-dimensional bosonic Yang-Mills excluding instanton contributions”. Hence, we support the recent conjecture by Drukker, Giombi, Ricci and Trancanelli on the 1/8 BPS Wilson loops on S 2 in the 4d \( \mathcal{N}=4 \) SYM.
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ArXiv ePrint: 0906.0638
On leave of absence from ITEP, 117218, Moscow, Russia. (Vasily Pestun)
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Pestun, V. Localization of the four-dimensional \( \mathcal{N}=4 \) SYM to a two-sphere and 1/8 BPS Wilson loops. J. High Energ. Phys. 2012, 67 (2012). https://doi.org/10.1007/JHEP12(2012)067
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DOI: https://doi.org/10.1007/JHEP12(2012)067