Strings in Bubbling Geometries and Dual Wilson Loop Correlators

TL;DR

This paper establishes a precise match between string actions in bubbling geometries and Wilson loop correlators in ${ m f N}=4$ SYM, providing explicit results for certain representations and geometries.

Contribution

It demonstrates the exact correspondence between minimal string actions in arbitrary genus bubbling geometries and Wilson loop correlators in large representations, including explicit calculations for rectangular Young tableaux.

Findings

Matching of string actions and Wilson loop correlators in bubbling geometries.

Explicit results for rectangular Young tableaux (genus one) cases.

Field theory calculations for correlators involving large and small Wilson loops.

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 ${\cal N}=4$ 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.