Correlation function of null polygonal Wilson loops with local operators

Abstract

We consider the correlator <W_n O(x)> of a light-like polygonal Wilson loop with n cusps with a local operator (like the dilaton or the chiral primary scalar) in planar N =4 super Yang-Mills theory. As a consequence of conformal symmetry, the main part of such correlator is a function F of 3n-11 conformal ratios. The first non-trivial case is n=4 when F depends on just one conformal ratio ζ. This makes the corresponding correlator one of the simplest non-trivial observables that one would like to compute for generic values of the `t Hooft coupling λ. We compute F(ζ,λ) at leading order in both the strong coupling regime (using semiclassical AdS5 x S5 string theory) and the weak coupling regime (using perturbative gauge theory). Some results are also obtained for polygonal Wilson loops with more than four edges. Furthermore, we also discuss a connection to the relation between a correlator of local operators at null-separated positions and cusped Wilson loop suggested in arXiv:1007.3243.

36 pages, 2 figures

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• The Wilson Loop -- Large Spin OPE Dictionary
• All-Loop Four-Point Aharony-Bergman-Jafferis-Maldacena Amplitudes from Dimensional Reduction of the Amplituhedron
• On correlation functions of Wilson loops, local and non-local operators
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• Integrated negative geometries in ABJM
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• Extremal Correlator of Three Vertex Operators for Circular Winding Strings in AdS5xS5
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• Wilson Loops with Lagrangians: Large Spin OPE and Cusp Anomalous Dimension Dictionary
• Holographic correlation functions of hexagon Wilson loops with one local operator
• Holographic Calculations of Euclidean Wilson Loop Correlator in Euclidean anti-de Sitter Space
• On semiclassical four-point correlators in AdS_5 x S^5