Conformal properties of four-gluon planar amplitudes and Wilson loops

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

642 citations recorded by the source corpus.

We present further evidence for a dual conformal symmetry in the four-gluon planar scattering amplitude in N=4 SYM. We show that all the momentum integrals appearing in the perturbative on-shell calculations up to four loops are dual to true conformal integrals, well defined off shell. Assuming that the complete off-shell amplitude has this dual conformal symmetry and using the basic properties of factorization of infrared divergences, we derive the special form of the finite remainder previously found at weak coupling and recently reproduced at strong coupling by AdS/CFT. We show that the same finite term appears in a weak coupling calculation of a Wilson loop whose contour consists of four light-like segments associated with the gluon momenta. We also demonstrate that, due to the special form of the finite remainder, the asymptotic Regge limit of the four-gluon amplitude coincides with the exact expression evaluated for arbitrary values of the Mandelstam variables.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/2ac11d5291e770bbe1f0258b0dde38faa502936e

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In Nuclear and High Energy Physics

1. S. Caron-Huot
2. L. Dixon
3. J. Drummond
4. L. Alday
5. N. Arkani-Hamed
6. F. Cachazo
7. J. Maldacena
8. R. Roiban

Citations in the corpus

• From correlation functions to scattering amplitudes (2010, background): “14) are quite complicated, their sum F (2) A can be found in a closed form thanks to the remarkable duality between MHV amplitudes and light-like Wilson loops [2, 3, 4].”
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory (2009, background): “At weak coupling however, it was found that light-like Wilson loops are dual to MHV amplitudes, as was demonstrated for n = 4, 5, 6 gluons scattering up to two-loop order [21, 22, 23].”
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes (2007, positive): “First of all, the finite part of the • four-gluon amplitude has been calculated up to three loops [1] • five-gluon amplitude has been calculated up to two loops [11] • n-gluon amplitude is known at one loop [30] In all these cases the results match those for the Wilson loops, found either by explici”
• Scattering amplitudes, Wilson loops and the string/gauge theory correspondence (2008, methodology): “Assuming the BDS ansatz holds and making use of the demonstrated equivalence of one-loop MHV amplitudes and light-like Wilson loops [105, 130] which will be discussed in detail in section 4, the prescription for computing scattering amplitudes at strong coupling can be written in purely geometrical ”
• Bootstrapping the three-loop hexagon (2011, background): “One of their most surprising properties is an equivalence with certain light-like Wilson loop configurations, for which there is strong empirical evidence at weak coupling, as well as general arguments originating from strong coupling [1, 2, 3, 4, 5, 6, 7, 8].”
• Hexagon functions and the three-loop remainder function (2013, background): “In particular, the amplitudes exhibit dual conformal symmetry and a duality to light-like polygonal Wilson loops [9–14].”
• Single-valued harmonic polylogarithms and the multi-Regge limit (2012, background): “Remarkably, the planar N = 4 super-Yang-Mills amplitudes are governed by a dual conformal symmetry acting on the xi [1, 2, 3, 4, 5, 6, 7].”
• A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon (2014, background): “The duality with Wilson loops [3, 4, 5, 6, 7, 8, 9] and the associated dual conformal symmetry [7, 10, 11, 12, 13] of the planar theory mean that only amplitudes with six or more external legs are non-trivial.”