Maths HEP Lunchtime Seminars: Scattering Amplitudes and Holomorphic Wilson Loops
18 February 2011 13:00 in CM221
I will introduce a complex analogue of the Wilson loop, which is defined on a complex curve, in holomorphic Chern-Simons theory and explain how the complete planar S-matrix of maximal supersymmetric Yang-Mills theory is just such a Wilson loop in twistor space. The dynamics of the theory are expressed through loop equations, describing how the expectation value of the Wilson loop varies as the curve is deformed. Particular deformations of the curve then lead to powerful methods for computing scattering amplitudes, including the all-loop BCFW recursion relations and the MHV vertex expansion. This provides a new and fundamental perspective on the scattering amplitude - Wilson loop duality and allows the S-matrix to be interpreted as a holomorphic analogue of a knot invariant.