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Scattering amplitudes and Wilson loops in twistor space.

Adamo, Tim and Bullimore, Mathew and Mason, Lionel and Skinner, David (2011) 'Scattering amplitudes and Wilson loops in twistor space.', Journal of physics A : mathematical and theoretical., 44 (45). p. 454008.


This paper reviews the recent progress in twistor approaches to Wilson loops, amplitudes and their duality for $\mathcal {N}=4$ super-Yang–Mills. Wilson loops and amplitudes are derived from first principles using the twistor action for maximally supersymmetric Yang–Mills theory. We start by deriving the MHV rules for gauge theory amplitudes from the twistor action in an axial gauge in twistor space, and show that this gives rise to the original momentum space version given by Cachazo, Svrček and Witten. We then go on to obtain from these the construction of the momentum twistor space loop integrand using (planar) MHV rules and show how it arises as the expectation value of a holomorphic Wilson loop in twistor space. We explain the connection between the holomorphic Wilson loop and certain light-cone limits of correlation functions. We give a brief review of other ideas in connection with amplitudes in twistor space: twistor-strings, recursion in twistor space, the Grassmannian residue formula for leading singularities and amplitudes as polytopes. This paper is an invited review for a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Scattering amplitudes in gauge theories'.

Item Type:Article
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Publisher statement:This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at
Date accepted:No date available
Date deposited:02 July 2018
Date of first online publication:20 October 2011
Date first made open access:No date available

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