Title:

Aspects of superconformal quantum field theory

Various Issues in Superconformal Quantum Field Theory in (mainly) four dimensions for N = 1,2,4 are discussed. Broadly these issues concern the constraints placed on scalar four point functions by superconformal symmetry and the information that they give concerning the operator product expansion. Where possible this information is verified from the point of view of three point functions (for N = 4) and of superconformal representation theory for N = 2,4. For N = 1 the chiral superfield four point function is computed and verified in a number of ways; involving a counting argument and superconformal integrals and from the point of view of the operator product expansion. For N = 2 two point functions for fields in the simplest nontrivial supermultiplet and fourpoint functions involving the scalar quasiprimary fields of this supermultiplet are discussed. For N = 4 the simplest supermultiplet containing the energy momentum tensor is similarly considered as for N = 2. Two point functions and three point functions, up to the energy momentum tensor three point function, are computed. Four point functions of the scalar quasiprimary fields (corresponding to chiral primary operators of scaling dimension 2) for this N = 4 supermultiplet are also investigated, revealing an interesting struture implied by superconformal symmetry and the operator product expansion. The operator product expansion is applied to these various scalar four point functions in the disguised form of a conformal partial wave expansion. A new method is applied and a new result in four dimensions is found for the conformal partial wave expansion. This result proves particularly useful for extracting detailed information about the operator product expansion contained in four point functions in four dimensions. It is also useful for extracting anomalous dimensions of operators as is done for the N = 4 chiral primary four point function at weak and strong coupling. The strong coupling result derives from the AdS/CFT correspondence and reveals interesting information which demonstates the decoupling phenomena for large 't Hooft coupling and large N from a purely algebraic viewpoint.
