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.
Highlights
Starting with the seminal work of [1] we have large classes of supersymmetric AdS4 × Y7 gravity backgrounds of M-theory that are associated with particular (2 + 1)dimensional supersymmetric gauge theories, typically Chern-Simons theories coupled to matter, that are believed to have a dual superconformal fixed point
The construction of the UV gauge theory usually relies on a dual description in terms of type IIA string theory, which in turn involves a choice of M-theory circle U(1)M acting on Y7; different choices can lead to different UV gauge theories that flow to the same IR superconformal fixed point
This Wilson loop is 1/2 BPS in a general N = 2 supersymmetric gauge theory on S3, as we review in section 2, and can be computed using the large N matrix model description
Summary
Starting with the seminal work of [1] we have large classes of supersymmetric AdS4 × Y7 gravity backgrounds of M-theory that are associated with particular (2 + 1)dimensional supersymmetric gauge theories, typically Chern-Simons theories coupled to matter, that are believed to have a dual superconformal fixed point. In the original papers on the ABJM theory [26, 30, 38,39,40,41] the supersymmetric Wilson loop for the gauge field around a Hopf circle S1 ⊂ S3 was studied This is 1/2 BPS, and is readily computed in the large N matrix model [26, 30]. Semi-classically, more precisely this will be a supersymmetric minimal surface Σ2 in Euclidean AdS4, with the VEV calculated via the regularized area of the string worldsheet Such a string must be pointlike in the internal space, and for the ABJM theory this is CP3 = S7/U(1)M.
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