Wilson loops on three-manifolds and their M2-brane duals

Abstract

We compute the large N limit of Wilson loop expectation values for a broad class of 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 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.

arXiv comment24 pages; v2: references and discussion of torus knots added

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• Aspects of Defects in 3d-3d Correspondence
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• Supersymmetric Wilson loops in two dimensions and duality
• Wilson Loops for M2- and M5-brane spaces
• Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions