Title:

Correlation functions, scattering amplitudes and the superconformal partial wave

In this thesis we explore aspects of correlation functions and scattering amplitudes in supersymmetric field theories. Firstly, we study correlation functions and scattering amplitudes in the perturbative regime of N=4 supersymmetric YangMills theory. Here we begin by giving a new method for computing the supercorrelation functions of the chiral part of the stresstensor supermultiplet by making use of twistor theory. We derive Feynman rules and graphical rules which involve a new set of building blocks which we can identify as a new class of N=4 offshell superconformal invariants. This class of offshell superconformal invariant is related to the known N=4 onshell superconformal invariant pertinent to planar scattering amplitudes. We then move onto the sixpoint treelevel NMHV scattering amplitude. Previous results are given in terms of a manifestly dual superconformal invariant basis called the Rinvariant. We define and analyse a generalisation of this invariant which contains half of the dual superconformal invariance. We apply it to the sixpoint treelevel NMHV scattering amplitude and find a new representation which manifestly contains half of the dual superconformal invariance and physical pole structure. This is in contrast to the Rinvariant basis which manifests symmetry properties but does not manifest physical pole structures. Finally, we find the superconformal partial wave for fourpoint correlation functions of scalar operators on a super Grassmannian space (the space of mnplanes in 2m2ndimensions) for theories with spacetime symmetry SU(m,m2n). This contains N=0,2,4 fourdimensional superconformal field theories in analytic superspace as well as a certain class of representations for the compact SU(2n) coset spaces. As an application we then specialise to N=4 supersymmetric YangMills theory and use these results to perform a detailed superconformal partial wave analysis of the fourpoint functions of arbitrary weight halfBPS operators. We discuss the nontrivial separation of protected and unprotected sectors for the <2222>, <2233> and <3333> cases in an SU(N) gauge theory at finite N (where < ijkl > = < tr(W^i)tr(W^j)tr(W^k)tr(W^l) >). The <2233> correlator predicts a nontrivial protected twist four sector for <3333> which we can completely determine using the knowledge that there is one such protected twist4 operator for each spin.
