Dualitites in quantum field theory from string theory

Abstract

Quantum field theory (QFT), is a powerful framework to study diverse phenomena in physics. The range of topics includes the interactions of elementary particles, the continuum limit of condensed matter systems defined on a lattice, models of the expanding universe, as well as quantum gravity. Despite its enormous breadth of applications, it is still quite poorly understood. From a pragmatic point of view, a generic QFT is well understood in the per-turbative regime, where one has a small expansion parameter or coupling constant. That we have a satisfactory understanding of QFTs in the weakly coupled regime, is highlighted by the fact that we have a single formalism, namely feynman diagrams, that can be applied to any weakly coupled theory. Conversely, there is no universal framework to understand non-perturbative and strong coupling phenomena. Instead, we have a distinct set of tools, which apply to distinct sets of very special theories, such as those with supersymmetry or topolog-ical theories. From this perspective, to understand the strong coupling dynamics of a QFT, is to develop a unique formalism that can be applied to solve a generic strongly coupled QFT. The reader should be warned that this thesis will not achieve such an ambitious goal. How-ever, it is good to keep this general philosophy in mind, as a broader motivation for some of the work presented. We will provide, instead, a collection of data points for particular sec-tors of strongly coupled QFTs that are under analytic control. One can hope that some day, these data points can provide the foundations for a more systematic and universal approach. From a more formal viewpoint, quantum field theory, as of yet, has no rigorous mathemati-cal basis. This is particularly bothersome, given the deep interconnections between ideas in modern mathematics and those of QFT [1]. The goal of this thesis is to introduce its reader to a few notable examples, where the former issue can be overcome. The unifying theme of all these examples is their relation to brane dynamics in string theory [2]. We will make extensive use of the string theory embedding of the QFTs under consideration, in order to illuminate their strong coupling dynamics.