Large charges on the Wilson loop in N=4 SYM. Part II. Quantum fluctuations, OPE, and spectral curve

We continue our study of large charge limits of the defect CFT defined by the half-BPS Wilson loop in planar N = 4 supersymmetric Yang-Mills theory. In this paper, we compute 1/J corrections to the correlation function of two heavy insertions of charge J and two light insertions, in the double scaling limit where the charge J and the 't Hooft coupling A are sent to infinity with the ratio J/root lambda fixed. Holographically, they correspond to quantum fluctuations around a classical string solution with large angular momentum, and can be computed by evaluating Green's functions on the worldsheet. We derive a representation of the Green's functions in terms of a sum over residues in the complexified Fourier space, and show that it gives rise to the conformal block expansion in the heavy-light channel. This allows us to extract the scaling dimensions and structure constants for an infinite tower of non-protected dCFT operators. We also find a close connection between our results and the semi-classical integrability of the string sigma model. The series of poles of the Green's functions in Fourier space corresponds to points on the spectral curve where the so-called quasi-momentum satisfies a quantization condition, and both the scaling dimensions and the structure constants in the heavy-light channel take simple forms when written in terms of the spectral curve. These observations suggest extensions of the results by Gromov, Schafer-Nameki and Vieira on the semiclassical energy of closed strings, and in particular hint at the possibility of determining the structure constants directly from the spectral curve.

Automated summary

This paper investigates the behavior of the defect CFT defined by the half-BPS Wilson loop in the large charge limit. Using holography, the authors compute 1/J corrections to the correlation function of heavy and light insertions and derive the scaling dimensions and structure constants for non-protected dCFT operators. They also find a close connection between their results and the semi-classical integrability of the string sigma model.