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Title:
Bootstrapping six-gluon scattering in planar N=4 Super-Yang-Mills theory through four loops
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Abstract:
Using the amplitude-Wilson loop correspondence, the operator product expansion for Wilson loops, multi-Regge factorization, and some assumptions about the analytic structure of the result, we have constructed the remainder function for the six-gluon MHV scattering amplitude at three and four loops. No multi-loop integrands are required. The answer can be expressed in terms of multiple polylogarithms in various kinematic regions, or expressed through functions defined iteratively by the Hopf algebra coproduct. In some kinematic regions, the 2, 3 and 4 loop coefficients have very similar numerical behavior, which is also similar to that observed at strong coupling. The BFKL eigenvalue, which controls the multi-Regge limit, can be extracted through the next-to-next-to-leading logarithmic order.
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