Integrated Correlators in \( \mathcal{N} \) = 4 \( SO(2N) \) Supersymmetric Yang-Mills Theory

Abstract

In this thesis, we use recent techniques to derive correlation functions of local operators in certain strongly-interacting conformal field theories that have weakly-coupled holographic dual descriptions through the Anti-de Sitter/Conformal Field Theory (AdS/CFT) Correspondence. The calculation of such correlation functions is of interest to illuminate local properties of these strongly interacting systems. In particular, we will focus on the ( \mathcal{N} ) = 4 Supersymmetric Yang-Mills theory with gauge group ( SO(2N) ), as well as ( SU(2) ) SYM and SQCD. We will use a combination of consistency conditions and exact results that are available for this theory. Such an exact result is the partition function of the theory placed on a round four-sphere and deformed by an ( \mathcal{N} ) = 2 supersymmetry-preserving mass parameter. Ordinarily, quantities such as the partition function are defined by infinite-dimensional integrals. However, due to supersymmetry, such infinite-dimensional integrals can be reduced to finite-dimensional ones that can be studied using the techniques of random matrix theory. We will be interested in derivatives of the free energy evaluated when the mass parameter vanishes, because these derivatives can be directly related to correlation functions of local operators. We will work in the large ( N ) and large 't Hooft coupling limit.