Constructing Exact Correlators In N=4 SYM Using Integrability

Abstract

This thesis is devoted to the study of correlation functions in N = 4 superconformal Yang- Mills theory. We focus on a class of four point functions for which we achieve formal results at finite coupling and explicit results at all-loops at weak coupling and strong coupling in the planar ‘t Hooft limit. We use three approaches to construct them. The first is the conformal OPE expansion for which we work out the necessary conformal data, scaling dimensions and structure constants, using integrability. The second uses a geometric decomposition of the four-punctured worldsheet into hexagonal patches. This renders the four-point function as a form factor series expansion and again thanks to integrability, the components of this series are completely worked out. In the third approach we adopt a bootstrap philosophy, we fix completely a non-trivial four-point function at all loops by assuming it satisfies certain properties which we learned from the weak coupling limit of our previous two approaches. We study the strong coupling limit in our second approach and obtain results that take the expected form for a holographic CFT dual to classical strings in AdS. Finally we compute non-planar corrections in a double scaling limit and manage to perform explicit all-genus resummations in special cases