Strings in Bubbling Geometries and Dual Wilson Loop Correlators

Abstract

We consider a fundamental string in a bubbling geometry of arbitrary genus dual to a half-supersymmetric Wilson loop in a general large representation $\mathbf{R}$ of the $SU(N)$ gauge group in $\mathcal{N}=4$ Supersymmetric Yang-Mills. We demonstrate, under some mild conditions, that the minimum value of the string classical action for a bubbling geometry of arbitrary genus precisely matches the correlator of a Wilson loop in the fundamental representation and one in a general large representation. We work out the case in which the large representation is given by a rectangular Young Tableau, corresponding to a genus one bubbling geometry, explicitly. We also present explicit results in the field theory for a correlator of two Wilson loops: a large one in an arbitrary representation and a "small" one in the fundamental, totally symmetric or totally antisymmetric representation.

40 pages + appendices, 9 figures, A new discussion of WL correlators using the product of characters formula, two new figures added. Typos fixed. Version that matches the published article

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Cited by in corpus (11)

• On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators
• Large $N$ and large representations of Schur line defect correlators
• Coherent state operators, giant gravitons, and gauge-gravity correspondence
• Ladder Limit for Correlators of Wilson Loops
• Excitations of bubbling geometries for line defects
• The Chern-Simons Current in Time Series of Knots and Links in Proteins
• Antisymmetric Wilson loops in N = 4 SYM: from exact results to non-planar corrections
• Interior analysis, stretched technique and bubbling geometries
• ADHM Wilson line defect indices
• Wilson loop and its correlators in the limit of large coupling constant
• Wilson loops correlators in defect $\mathcal{N}=4$ SYM