Exact 1/4 BPS Loop - Chiral Primary Correlator

Correlation functions of 1/4 BPS Wilson loops with the infinite family of 1/2 BPS chiral primary operators are computed in $\mathcal{N}=4$ super Yang-Mills theory by summing planar ladder diagrams. Leading loop corrections to the sum are shown to vanish. The correlation functions are also computed in the strong-coupling limit by examining the supergravity dual of the loop-loop correlator. The strong coupling result is found to agree with the extrapolation of the planar ladders. The result is related to known correlators of 1/2 BPS Wilson loops and 1/2 BPS chiral primaries by a simple re-scaling of the coupling constant, similar to an observation of Drukker, hep-th/0605151, for the case of the 1/4 BPS loop vacuum expectation value.