Abstract
We compute correlation functions of protected primaries on the 1/2-BPS Wilson loop in mathcal{N}=4 super Yang-Mills theory at weak coupling. We first perform direct perturbative computation at one loop in the planar limit and present explicit formulae for general two-, three- and four-point functions. The results for two- and three-point functions as well as four-point functions in special kinematics are in perfect agreement with the localization computation performed in arXiv:1802.05201. We then analyze the results in view of the integrability-based approach called “hexagonalization”, which was introduced previously to study the correlation functions in the absence of the Wilson loop. In this approach, one decomposes the correlator into fundamental building blocks called “hexagons”, and glues them back together by summing over the intermediate states. Through the comparison, we conjecture that the correlation functions on the Wilson loop can be computed by contracting hexagons with boundary states, where each boundary state represents a segment of the Wilson loop. As a byproduct, we make predictions for the large-charge asymptotics of the structure constants on the Wilson loop. Along the way, we refine the conjecture for the integrability-based approach to the general non-BPS structure constants on the Wilson loop, proposed originally in arXiv:1706.02989.
Highlights
Analyze the higher-dimensional gauge theories using the techniques of the two-dimensional field theories
We conjecture that the correlation functions on the Wilson loop can be computed by contracting hexagons with boundary states, where each boundary state represents a segment of the Wilson loop
The 1/2-BPS Wilson loop is a supersymmetric generalization of the ordinary Wilson loop which preserves the largest amount of supersymmetries
Summary
We consider the correlators on the straight line As explained above, such correlators have direct relation to the defect CFT data, see (2.36) and (3.35) for final results. The idea of computing the three-point functions on the Wilson loop from hexagons was proposed originally in [43]. We analyze the four-point function in a similar fashion; namely we propose that it can be computed by gluing two hexagons and four boundary states and multiplying a nontrivial cross-ratio-dependent weight factor, which was first determined in the study of correlators of single-trace operators in [17].
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