Abstract
We study the large charge sector of the defect CFT defined by the half-BPS Wilson loop in planar N = 4 supersymmetric Yang-Mills theory. Specifically, we consider correlation functions of two large charge insertions and several light insertions in the double-scaling limit where the ’t Hooft coupling λ and the large charge J are sent to infinity, with the ratio J/ sqrt{lambda } held fixed. They are holographically dual to the expectation values of light vertex operators on a classical string solution with large angular momentum, which we evaluate in the leading large J limit. We also compute the two-point function of large charge insertions by evaluating the on-shell string action, supplemented by the boundary terms that generalize the one introduced by Drukker, Gross and Ooguri for the Wilson loop without insertions. For a special class of correlation functions, we reproduce the string results from field theory by using supersymmetric localization. The results are given by correlation functions in an “emergent” matrix model whose matrix size is proportional to J and whose spectral curve coincides with that of the classical string. Similar matrix models appeared in the study of extremal correlators in rank-1 mathcal{N} = 2 superconformal field theories, but our results hold also for non-extremal cases.
Highlights
We study the large charge sector of the defect CFT defined by the half-BPS Wilson loop in planar N = 4 supersymmetric Yang-Mills theory
They are holographically dual to the expectation values of light vertex operators on a classical string solution with large angular momentum, which we evaluate in the leading large J limit
Defect operator insertions on the Wilson loop are dual to fluctuations of the string about the AdS2 geometry, and their correlation functions at strong coupling can be computed holographically by evaluating Witten diagrams in the string sigma model perturbation theory
Summary
This section introduces the defect CFT observables we will analyze in this paper. First, our conventions for N = 4 SYM: we work in Euclidean signature and use the standard. Wline N =4 SYM = 1, differs from eq (2.2) due to a “conformal anomaly” [45, 46], but the defect correlators on the circle and line, when normalized by the corresponding Wilson loop operator without insertions, behave in the standard way under conformal transformations. This lets us determine, to leading order, the normalized higher-point correlators. Because the light topological operators, Φ , truncate to linear combinations of powers of Z and Zat leading order
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