Bubbling Calabi-Yau geometry from matrix models

Abstract

We study bubbling geometry in topological string theory. Specifically, we analyse Chern-Simons theory on both the 3-sphere and lens spaces in the presence of a Wilson loop insertion of an arbitrary representation. For each of these three manifolds we formulate a multi-matrix model whose partition function is the vev of the Wilson loop and compute the spectral curve. This spectral curve is the reduction to two dimensions of the mirror to a Calabi-Yau threefold which is the gravitational dual of the Wilson loop insertion. For lens spaces the dual geometries are new. We comment on a similar matrix model which appears in the context of Wilson loops in AdS/CFT.

30 pages; v.2 reference added, minor corrections

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Cited by in corpus (10)

• Wilson loop correlators at strong coupling: from matrices to bubbling geometries
• Spectral curves, emergent geometry, and bubbling solutions for Wilson loops
• Chern-Simons theory on L(p,q) lens spaces and Localization
• M5-branes and Wilson Surfaces in AdS${}_7$/CFT${}_6$ Correspondence
• Large rank Wilson loops in N=2 superconformal QCD at strong coupling
• Wilson loops and its correlators with chiral operators in $\mathcal{N}=2,4$ SCFT at large $N$
• Comments on Higher Rank Wilson Loops in $\mathcal{N}=2^{\ast }$
• Wilson loop and its correlators in the limit of large coupling constant
• Toward the construction of the general multi-cut solutions in Chern-Simons Matrix Models
• Aspects géométriques et intégrables des modèles de matrices aléatoires