Spectral curves, emergent geometry, and bubbling solutions for Wilson loops

Abstract

We study the supersymmetric circular Wilson loops of N=4 super Yang-Mills in large representations of the gauge group. In particular, we obtain the spectral curves of the matrix model which captures the expectation value of the loops. These spectral curves are then proven to be precisely the hyperelliptic surfaces that characterize the bubbling solutions dual to the Wilson loops, thus yielding an example of a geometry emerging from an eigenvalue distribution. We finally discuss the Wilson loop expectation value from the matrix model and from supergravity.

27 pages, 2 figures; v2: references added

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Cited by in corpus (36)

• A supermatrix model for N=6 super Chern-Simons-matter theory
• Correlators of local operators and 1/8 BPS Wilson loops on S^2 from 2d YM and matrix models
• Probing N=4 SYM With Surface Operators
• The Spectrum of Excitations of Holographic Wilson Loops
• Wilson loop correlators at strong coupling: from matrices to bubbling geometries
• Exact results for Wilson loops in arbitrary representations
• Half-BPS supergravity solutions and superalgebras
• M-theory Solutions Invariant under $D(2,1;\gamma )\oplus D(2,1;\gamma )$
• Entanglement entropy vs. free energy in IIB supergravity duals for 5d SCFTs
• Notes on supersymmetric Wilson loops on a two-sphere
• A maximally supersymmetric Kondo model
• Localization and AdS/CFT Correspondence
• Review of AdS/CFT Integrability, Chapter IV.1: Aspects of Non-Planarity
• Exact probes of orientifolds
• Connected correlator of 1/2 BPS Wilson loops in $\mathcal{N}=4$ SYM
• Entanglement entropy of Wilson surfaces from bubbling geometries in M-theory
• Exact $\mathcal{N}=2^{\ast }$ Schur line defect correlators
• Boundary condition for D-brane from Wilson loop, and gravitational interpretation of eigenvalue in matrix model in AdS/CFT correspondence
• Large $N$ and large representations of Schur line defect correlators
• Geometry of open strings ending on backreacting D3-branes
• Strings in Bubbling Geometries and Dual Wilson Loop Correlators
• Gravity and On-Shell Probe Actions
• Phase Transition of Anti-Symmetric Wilson Loops in $\mathcal{N}=4$ SYM
• Excitations of bubbling geometries for line defects
• BPS Wilson loops in N=4 SYM: Examples on hyperbolic submanifolds of space-time
• Holographic entanglement entropy of surface defects
• Antisymmetric Wilson loops in N = 4 SYM: from exact results to non-planar corrections
• Entanglement entropy of Wilson loops: Holography and matrix models
• Wilson loops in antisymmetric representations from localization in supersymmetric gauge theories
• Wilson loops and its correlators with chiral operators in $\mathcal{N}=2,4$ SCFT at large $N$
• ADHM Wilson line defect indices
• Exact M-Theory Solutions, Integrable Systems, and Superalgebras
• Comments on Higher Rank Wilson Loops in $\mathcal{N}=2^{\ast }$
• Wilson loop and its correlators in the limit of large coupling constant
• 't Hooft Operators on an Interface and Bubbling D5-Branes
• Solving $\mathcal{N}=4$ SYM BCFT matrix models at large $N$