Localization of the four-dimensional N=4 SYM to a two-sphere and 1/8 BPS Wilson loops

Abstract

We localize the four-dimensional N=4 super Yang-Mills theory on a four-sphere to the two-dimensional constrained Hitchin/Higgs-Yang-Mills (cHYM) theory on a two-sphere S^2. We show that expectation values of certain 1/8 BPS supersymmetric Wilson loops on S^2 in the 4d N=4 SYM is captured by the 2d cHYM theory. We further argue that expectation values 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 N=4 SYM.

49 pages; v3: typos corrected

References in corpus (6)

• Supersymmetric Wilson loops on S^3
• Higgs Bundles, Gauge Theories and Quantum Groups
• Notes on supersymmetric Wilson loops on a two-sphere
• Correlators of supersymmetric Wilson-loops, protected operators and matrix models in N=4 SYM
• Calibrated Surfaces and Supersymmetric Wilson Loops
• Ten-dimensional super-Yang-Mills with nine off-shell supersymmetries

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