Scattering amplitudes and Wilson loops in twistor space
Abstract
This paper reviews the recent progress in twistor approaches to Wilson loops, amplitudes and their duality for {N}=4 superYangMills. Wilson loops and amplitudes are derived from first principles using the twistor action for maximally supersymmetric YangMills 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 lightcone limits of correlation functions. We give a brief review of other ideas in connection with amplitudes in twistor space: twistorstrings, 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’.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 November 2011
 DOI:
 10.1088/17518113/44/45/454008
 arXiv:
 arXiv:1104.2890
 Bibcode:
 2011JPhA...44S4008A
 Keywords:

 High Energy Physics  Theory
 EPrint:
 62 pages, 15 figures. v2: typos corrected, additional discussions and references added