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Bootstrapping the three-loop hexagon
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DOI：10.1007/JHEP11(2011)023.png)
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Abstract
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We consider the hexagonal Wilson loop dual to the six-point MHV amplitude in planar N = 1 super Yang-Mills theory. We apply constraints from the operator product expansion in the near-collinear limit to the symbol of the remainder function at three loops. Using these constraints, and assuming a natural ansatz for the symbol's entries, we determine the symbol up to just two undetermined constants. In the multi-Regge limit, both constants drop out from the symbol, enabling us to make a non-trivial confirmation of the BFKL prediction for the leading-log approximation. This result provides a strong consistency check of both our ansatz for the symbol and the duality between Wilson loops and MHV amplitudes. Furthermore, we predict the form of the full three-loop remainder function in the multi-Regge limit, beyond the leading-log approximation, up to a few constants representing terms not detected by the symbol. Our results confirm an all-loop prediction for the real part of the remainder function in multi-Regge 3 -> 3 scattering. In the multi-Regge limit, our result for the remainder function can be expressed entirely in terms of classical polylogarithms. For generic six-point kinematics other functions are required.
Keywords:
Supersymmetric gauge theory
Extended Supersymmetry
Conformal and W Symmetry
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5.5
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3.9W
Citations:
13.7W
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