Hidden conformal symmetry of gluon amplitudes and Wilson loops
Seminar Room 1, Newton Institute
I will summarise recent developments which indicate there is a hidden confomal symmetry of planar gluon scattering amplitudes in N=4 SYM. I will show that the momentum integrals appearing in the four-gluon scattering amplitude up to four loops are conformal when written in terms of dual coordinates. Then we will discuss a relation between gluon scattering amplitudes and Wilson loops orginally proposed by Alday and Maldacena at strong coupling. I will show evidence that this relation also holds at weak coupling and present a one-loop and two-loop confirmation of this result. We also analyse the conformal Ward identities satisfied by the Wilson loop and propose their all-order form. We show that the Bern-Dixon-Smirnov ansatz for the all-order form of the MHV amplitudes is the unique solution of the Ward identity for the Wilson loop (up to a function of conformal invariants which appear at six points and beyond) providing further evidence of a hidden conformal symmetry.
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