The Geometry of Scattering Amplitudes (12w5053)
Nima Arkani-Hamed (Institute for Advanced Study)
Zvi Bern (University of California at Los Angeles)
Alexander Goncharov (Yale University)
Lionel Mason (Oxford University)
David Skinner (Perimeter Institute for Theoretical Physics)
Although much of the recent progress has its origins in Witten's introduction of twistor-string theory, many of the most important developments have occurred in the last two or three years. These include the use of $AdS/CFT$ to probe the strong-coupling regime, and the associated representations of scattering amplitudes as minimal surfaces in $AdS_5$ or as piecewise null Wilson loops in space-time. In just the past year, the introduction of momentum twistors, the Grassmannian representation of amplitudes and their leading singularities, and the realisation that the planar amplitudes possess a Yangian symmetry have significantly increased both our understanding of and ability to compute planar amplitudes in planar $N=4$ sYM .
Developments continue apace with the recent construction of the all-loop integrand, and the twistor Wilson-loop correspondence discovered only in the last few weeks. Other themes that seem set to play an increasingly important role in future developments include, firstly, the close relation between quantum corrections to the amplitudes and motivic structures of polylogarithms together with their connection to Grassmannians and moduli spaces of pointed curves, secondly, the BCJ relations that intriguingly hint at a deep relation between scattering amplitudes in Yang-Mills and gravity, and thirdly, the quantization of the Hitchin systems that are related to the strong-coupling limit of the amplitudes.