Half-BPS Wilson loop and AdS${}_2$/CFT${}_1$

Abstract

We study correlation functions of local operator insertions on the 1/2-BPS Wilson line in $\mathcal{N}=4$ super Yang-Mills theory. These correlation functions are constrained by the 1d superconformal symmetry preserved by the 1/2-BPS Wilson line and define a defect CFT${}_1$ living on the line. At strong coupling, a set of elementary operator insertions with protected scaling dimensions correspond to fluctuations of the dual fundamental string in AdS${}_5\times S^5$ ending on the line at the boundary and can be thought of as light fields propagating on the AdS${}_2$ worldsheet. We use AdS/CFT techniques to compute the tree-level AdS${}_2$ Witten diagrams describing the strong coupling limit of the four-point functions of the dual operator insertions. Using the OPE, we also extract the leading strong coupling corrections to the anomalous dimensions of the "two-particle" operators built out of elementary excitations. In the case of the circular Wilson loop, we match our results for the 4-point functions of a special type of scalar insertions to the prediction of localization to 2d Yang-Mills theory.

29 pages, 2 figures. v5: typos corrected

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