The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude

By J. Drummond, J. Henn, G. Korchemsky, E. Sokatchev. 2007

195 citations recorded by the source corpus.

Abstract As a test of the gluon scattering amplitude/Wilson loop duality, we evaluate the hexagonal light-like Wilson loop at two loops in N = 4 super-Yang–Mills theory. We compare its finite part to the Bern–Dixon–Smirnov (BDS) conjecture for the finite part of the six-gluon amplitude. We find that the two expressions have the same behavior in the collinear limit, but they differ by a non-trivial function of the three (dual) conformally invariant variables. This implies that either the BDS conjecture or the gluon amplitude/Wilson loop duality fails for the six-gluon amplitude, starting from two loops. Our results are in qualitative agreement with the analysis of Alday and Maldacena of scattering amplitudes with infinitely many external gluons.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/12485c896445f96f5027ba9f50116ff1c019f69c

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In Nuclear and High Energy Physics

1. S. Caron-Huot
2. L. Dixon
3. J. Drummond
4. L. Alday
5. J. Maldacena
6. P. Vieira
7. N. Arkani-Hamed
8. A. Sever

Citations in the corpus

• Heptagons from the Steinmann cluster bootstrap (2016, background): “Starting at six points, the BDS ansatz receives corrections from finite functions of dual conformal invariants [25, 26, 28, 29].”
• An operator product expansion for polygonal null Wilson loops (2010, methodology): “Here we have checked this prediction with the only available direct computation in the literature, the two loop hexagon [6, 13, 14, 20, 21].”
• Scattering amplitudes, Wilson loops and the string/gauge theory correspondence (2008, methodology): “Thorough numerical tests of this relation were carried out in [145] with the result that equation (4.”
• The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM (2010, background): “In a parallel development, an amazing hidden symmetry of planar N = 4 SYM—dual conformal invariance—was noticed first in multi-loop perturbative calculations [17] and then at strong coupling [18], leading to a remarkable connection between null-polygonal Wilson loops and scattering amplitudes [18–27”
• From correlation functions to scattering amplitudes (2010, background): “This dual conformal symmetry, or rather its anomalous version [6, 18], was instrumental in explaining the so-called BDS ansatz for MHV amplitudes [15].”
• An analytic result for the two-loop hexagon Wilson loop in N = 4 SYM (2010, methodology): “At weak coupling, the agreement between the light-like Wilson loop and the (parityeven part of the) MHV amplitude has been verified for the one-loop four-edged [13] and n-edged [14] Wilson loops, and for the two-loop four-edged [15], five-edged [16] and sixedged [6, 17] Wilson loops.”
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory (2009, background): “Indeed the two-loop, six-point calculations of [26, 28, 29] showed that the amplitude and the Wilson loop both differ from the BDS conjecture by the same function of dual conformal invariants.”
• Bootstrapping the three-loop hexagon (2011, background): “Here FWL n ,1−loop is the one-loop result for F WL n , while Rn is the ‘remainder function’, which is a function only of conformal cross ratios and becomes non-vanishing at two loops [5].”