Wilson loops and the geometry of matrix models in AdS4/CFT3

Abstract

Abstract We study a general class of supersymmetric AdS4 × Y 7 solutions of M-theory that have large N dual descriptions as $ \mathcal{N} $ = 2 Chern-Simons-matter theories on S 3. The Hamiltonian function h M for the M-theory circle, with respect to a certain contact structure on Y 7, plays an important role in the duality. We show that an M2-brane wrapping the M-theory circle, giving a fundamental string in AdS4, is supersymmetric precisely at the critical points of h M , and moreover the value of this function at the critical point determines the M2-brane action. Such a configuration determines the holographic dual of a BPS Wilson loop for a Hopf circle in S 3, and leads to an effective method for computing the Wilson loop on both sides of the correspondence in large classes of examples. We find agreement in all cases, including for several infinite families, and moreover we find that the image h M (Y 7) determines the range of support of the eigenvalues in the dual large N matrix model, with the critical points of h M mapping to points where the derivative of the eigenvalue density is discontinuous.