Bootstrapping the threeloop hexagon
Abstract
We consider the hexagonal Wilson loop dual to the sixpoint MHV amplitude in planar mathcal{N} = 4 super YangMills theory. We apply constraints from the operator product expansion in the nearcollinear 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 multiRegge limit, both constants drop out from the symbol, enabling us to make a nontrivial confirmation of the BFKL prediction for the leadinglog 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 threeloop remainder function in the multiRegge limit, beyond the leadinglog approximation, up to a few constants representing terms not detected by the symbol. Our results confirm an allloop prediction for the real part of the remainder function in multiRegge 3 → 3 scattering. In the multiRegge limit, our result for the remainder function can be expressed entirely in terms of classical polylogarithms. For generic sixpoint kinematics other functions are required.
 Publication:

Journal of High Energy Physics
 Pub Date:
 November 2011
 DOI:
 10.1007/JHEP11(2011)023
 arXiv:
 arXiv:1108.4461
 Bibcode:
 2011JHEP...11..023D
 Keywords:

 Supersymmetric gauge theory;
 Extended Supersymmetry;
 Conformal and W Symmetry;
 High Energy Physics  Theory
 EPrint:
 36 pages, 1 figure, plus 8 ancillary files containing symbols of functions