Comments on Higher Rank Wilson Loops in $\mathcal{N}=2^{\ast }$

Abstract

For $\mathcal{N}=2^{\ast }$ theory with $U(N)$ gauge group we evaluate expectation values of Wilson loops in representations described by a rectangular Young tableau with $n$ rows and $k$ columns. The evaluation reduces to a two-matrix model and we explain, using a combination of numerical and analytical techniques, the general properties of the eigenvalue distributions in various regimes of parameters $(N,\lambda ,n,k)$ where $\lambda$ is the 't Hooft coupling. In the large $N$ limit we present analytic results for the leading and sub-leading contributions. In the particular cases of only one row or one column we reproduce previously known results for the totally symmetry and totally antisymmetric representations. We also extensively discusss the $\mathcal{N}=4$ limit of the $\mathcal{N}=2^{\ast }$ theory. While establishing these connections we clarify aspects of various orders of limits and how to relax them; we also find it useful to explicitly address details of the genus expansion. As a result, for the totally symmetric Wilson loop we find new contributions that improve the comparison with the dual holographic computation at one loop order in the appropriate regime.

28 pages, 4 figures. v2: References added. v3: More references, JHEP version

References in corpus (9)

• Holographic Wilson Loops
• Wilson Loops of Anti-symmetric Representation and D5-branes
• The Spectrum of Excitations of Holographic Wilson Loops
• A prediction for bubbling geometries
• Bubbling Calabi-Yau geometry from matrix models
• Quantum String Test of Nonconformal Holography
• Symmetric Wilson Loops beyond leading order
• Higher Rank ABJM Wilson Loops from Matrix Models
• Spectra of Certain Holographic ABJM Wilson Loops in Higher Rank Representations

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• Antisymmetric Wilson loops in N = 4 SYM: from exact results to non-planar corrections