Exact 1/4 BPS Loop - Chiral Primary Correlator

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.

Figures (4)

• Figure 1: The leading planar contribution to $\langle W[C_{\tiny 1/4}]~{\rm Tr}(\Phi_3+i\Phi_4)^J \rangle$. There are $J$ lines connecting the chiral primary on the left with the circular Wilson loop on the right.
• Figure 2: A ladder diagram of $\langle W[C_{\tiny 1/4}]~{\rm Tr}(\Phi_3+i\Phi_4)^J \rangle$. The "rungs" represent the combined gauge field and scalar propagator. For clarity, $J$ has been set to 2.
• Figure 3: The one-loop radiative corrections to $\langle W[C_{\tiny 1/4}]~{\rm Tr}(\Phi_3+i\Phi_4)^J \rangle$. Only an adjacent pair of the $J$ scalar lines are shown.
• Figure 4: The string worldsheets of two widely separated Wilson loops exchange a supergravity mode dual to a chiral primary operator.