Null Wilson loops with a self-crossing and the Wilson loop/amplitude conjecture

Abstract

The present study illuminates the relation between null cusped Wilson loops and their corresponding amplitudes. We find that, compared to the case with no self-crossing, the one loop expectation value of a self-intersecting Wilson loop develops an additional 1/εsingularity associated to the intersection. Interestingly, the same 1/εpole exists in the finite part of the one loop amplitude, appearing in the BDS conjecture, at the corresponding kinematic limit. At two loops, we explore the behaviour of the remainder function R, encoding the deviation of the amplitude from the BDS conjecture. By analysing the renormalisation group equations for the Wilson loop with a simple self-crossing, we argue that, when approaching the configuration with a self-crossing (u_2 \to 1, u_1\approx u_3), R diverges in the imaginary direction like R ~ i π\log^3(1-u_2). This behaviour can be attributed to the non-trivial analytic continuation needed when passing from the Euclidean to the physical region and suggests that R has a branch cut in the negative u_2 axis when the two other cross ratios are approximately equal (u_1 \approx u_3).

23 pages, 1 figure, typos corrected,references added

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Cited by in corpus (15)

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• Two and three-point correlators of operators dual to folded string solutions at strong coupling
• Simplicity of Polygon Wilson Loops in N=4 SYM
• Multi-soft theorems in Gauge Theory from MHV Diagrams
• Wilson loop remainder function for null polygons in the limit of self-crossing
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• Hexagon remainder function in the limit of self-crossing up to three loops
• A Surprise in the Amplitude/Wilson Loop Duality
• All orders results for self-crossing Wilson loops mimicking double parton scattering
• A Two-Loop Four-Point Form Factor at Function Level
• Conformal geometry of null hexagons for Wilson loops and scattering amplitudes
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Holographic interpolations of defect CFTs
• A new higher-spin theory of supergravity in 2+1 dimensions