Strings in Bubbling Geometries and Dual Wilson Loop Correlators

Understand

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.