Wilson Loops in N=4 SYM and Fermion Droplets

Abstract

The matrix models which are conjectured to compute the circle Wilson loop and its correlator with chiral primary operators are mapped onto normal matrix models. A fermion droplet picture analogous to the well-known one for chiral primary operators is shown to emerge in the large N limit. Several examples are computed. We find an interesting selection rule for the correlator of a single trace Wilson loop with a chiral primary operator. It can be non-zero only if the chiral primary is in a representation with a single hook. We show that the expectation value of the Wilson loop in a large representation labelled by a Young diagram with a single row has a first order phase transition between a regime where it is identical to a large column representation and a regime where it is a large wrapping number single trace Wilson loop.

32 pages, 2 figures

References in corpus (5)

• Wilson Loops of Anti-symmetric Representation and D5-branes
• Small deformations of supersymmetric Wilson loops and open spin-chains
• Normal random matrix ensemble as a growth problem
• Computing Wilson lines with dielectric branes
• Semiclassical evolution of the spectral curve in the normal random matrix ensemble as Whitham hierarchy

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• Two universal results for Wilson loops at strong coupling
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• Exact 1/4 BPS Loop - Chiral Primary Correlator
• Anomalous Dimensions from a Spinning D5-Brane
• Correlators, Probabilities and Topologies in N=4 SYM
• UV-divergences of Wilson Loops for Gauge/Gravity Duality
• On 1/2-BPS Wilson-'t Hooft loops
• Near BPS Wilson Loop in beta-deformed Theories
• Boundary condition for D-brane from Wilson loop, and gravitational interpretation of eigenvalue in matrix model in AdS/CFT correspondence
• Operator Product Expansion of Wilson surfaces from M5-branes