| Summary: | 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 Yang-Mills theory. Here we begin by giving a new method for computing the supercorrelation functions of the chiral part of the stress-tensor 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 off-shell superconformal invariants. This class of off-shell superconformal invariant is related to the known N=4 on-shell superconformal invariant pertinent to planar scattering amplitudes. We then move onto the six-point tree-level NMHV scattering amplitude. Previous results are given in terms of a manifestly dual superconformal invariant basis called the R-invariant. We define and analyse a generalisation of this invariant which contains half of the dual superconformal invariance. We apply it to the six-point tree-level 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 R-invariant basis which manifests symmetry properties but does not manifest physical pole structures. Finally, we find the superconformal partial wave for four-point correlation functions of scalar operators on a super Grassmannian space (the space of m|n-planes in 2m|2n-dimensions) for theories with space-time symmetry SU(m,m|2n). This contains N=0,2,4 four-dimensional 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 Yang-Mills theory and use these results to perform a detailed superconformal partial wave analysis of the four-point functions of arbitrary weight half-BPS operators. We discuss the non-trivial 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 non-trivial protected twist four sector for <3333> which we can completely determine using the knowledge that there is one such protected twist-4 operator for each spin.
|
|---|
