PhDIn 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 elementsQueen Mary University of London Centre for Research in String
Theor
