Four Dimensional Superconformal Field Theories From String Theory.
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In this work, we discuss four dimensional SCFTs which descend from string theory and M-theory. These SCFTs arise naturally from stacks of string and M- theory branes and are useful tools for studying various phenomena in four dimensional quantum eld theory. In the rst chapter we give a brief non-technical introduction and historical background to string theory and supersymmetry which motivates the study of these elds. The second chapter contains a review of background material related to supersymmetric gauge theories and conformal eld theories. In this context, we discuss anomalies and moduli spaces, and their utility in quantum eld theory. Additionally, we introduce how to construct some exotic eld theories by coupling non-Lagrangian sectors to Lagrangian theories. In the third chapter, we examine a special family of four dimensional N = 2 SCFTs that are obtained by wrapping the six dimensional (2; 0) theory on a Riemann surface. We derive some properties of these theories and discover various dualities involving them. We then give a brief introduction to the superconformal index and use it to examine the operator content of these theories. Finally we construct new N = 1 gauge theories by coupling these N = 2 theories to N = 1 matter and examining the resulting RG ows. In the fourth chapter, we discuss the problem of counting chiral primary gaugeinvariant operators in D-brane world-volume gauge theories. These theories live on a at stack of D3-branes with various transverse toric geometries. We investigate the six dimensional transverse space, as well as the moduli space and chiral ring of the world-volume theory, and nd previously unknown relationships between these elements
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