Exact 1/4 BPS Loop - Chiral Primary Correlator

TL;DR

This paper computes correlation functions between 1/4 BPS Wilson loops and 1/2 BPS chiral primaries in $ ext{N}=4$ super Yang-Mills, demonstrating agreement between weak and strong coupling results and relating them to known BPS correlators.

Contribution

It provides the first explicit calculation of these correlators using planar ladder diagrams and supergravity duals, revealing a simple coupling re-scaling relation.

Findings

Planar ladder diagrams sum to the correlator with vanishing leading loop corrections.

Strong coupling results match the extrapolated ladder sum.

Correlation functions relate to known BPS correlators via coupling re-scaling.

Abstract

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.