Abstract
We compute the large N limit of Wilson loop expectation values for a broad class of \( \mathcal{N}=2 \) supersymmetric gauge theories defined on a general class of background three-manifolds M 3, diffeomorphic to S 3. We find a simple closed formula which depends on the background geometry only through a certain supersymmetric Killing vector field. The supergravity dual of such a Wilson loop is an M2-brane wrapping the M-theory circle, together with a complex curve Σ2 in a self-dual Einstein manifold M 4, whose conformal boundary is M 3. We show that the regularized action of this M2-brane also depends only on the supersymmetric Killing vector, precisely reproducing the large N field theory computation.
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Farquet, D., Sparks, J. Wilson loops on three-manifolds and their M2-brane duals. J. High Energ. Phys. 2014, 173 (2014). https://doi.org/10.1007/JHEP12(2014)173
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DOI: https://doi.org/10.1007/JHEP12(2014)173