On planar gluon amplitudes/Wilson loops duality

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

457 citations recorded by the source corpus.

There is growing evidence that on-shell gluon scattering amplitudes in planar N=4 SYM theory are equivalent to Wilson loops evaluated over contours consisting of straight, light-like segments defined by the momenta of the external gluons. This equivalence was first suggested at strong coupling using the AdS/CFT correspondence and has since been verified at weak coupling to one loop in perturbation theory. Here we perform an explicit two-loop calculation of the Wilson loop dual to the four-gluon scattering amplitude and demonstrate that the relation holds beyond one loop. We also propose an anomalous conformal Ward identity which uniquely fixes the form of the finite part (up to an additive constant) of the Wilson loop dual to four- and five-gluon amplitudes, in complete agreement with the BDS conjecture for the multi-gluon MHV amplitudes

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d9ddf0f7f52f8674ec297286cf7726ad65e798cb

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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. N. Arkani-Hamed
7. F. Cachazo
8. J. Henn

Citations in the corpus

• A Note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix (2008, background): “Very interestingly, it was shown in [7, 8] that by performing dual conformal transformations on the lightlike Wilson loops in the N = 4 theory one can derive anomalous Ward identities, whose solution is equal to the BDS ansatz [24] for the exponentiated form of the n-point MHV scattering amplitude o”
• An analytic result for the two-loop hexagon Wilson loop in N = 4 SYM (2010, methodology): “The two-loop coefficient w (2) n has been computed analytically for n = 4 [15] and n = 5 [16] and numerically for n = 6 [17] and n = 7, 8 [18].”
• Holography from Conformal Field Theory (2009, background): “However, the only amplitudes for which there is a fairly strong all-orders understanding are the on-shell four and five point functions [15], which are highly constrained by symmetry [16], whereas we need at least the off-shell fourpoint function.”
• 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.”
• From correlation functions to scattering amplitudes (2010, background): “It was first proposed at strong coupling [2] and soon afterwards also observed at weak coupling, first at one loop [3, 4], followed by extensive two-loop tests [5, 6, 7, 8].”
• Motivic amplitudes and cluster coordinates (2013, background): “A very special feature of SYM theory in the planar limit is that all amplitudes are invariant under conformal transformations in this dual space-time [14–21] It is often useful, especially when one is interested in discussing aspects of conformal symmetry, to compactify the space-time.”
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory (2009, background): “For example, the dual conformal symmetry is expected to be broken in a way governed by an anomalous dual conformal Ward identity [33, 37].”
• Comments on gluon scattering amplitudes via AdS/CFT (2007, background): “On the other hand, recently [5,10,6] an interesting equivalence between two seemingly different observables was considered: scattering amplitudes and Wilson loops.”
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude (2007, methodology): “In [11, 12] we confirmed these relations by an explicit two-loop calculation of the divergent part of W4 and W5.”
• Bootstrapping an NMHV amplitude through three loops (2014, background): “In addition, empirical results have led to the discovery of many hidden properties of planar N = 4 SYM, such as dual (super)conformal invariance [8–12], and the amplitude-Wilson-loop duality [11, 13–16].”