String theory, supergravity and four-dimensional field theories.

Abstract

In this dissertation I present some of the basic computations in string theory and supergravity with an eye for their use in AdS/CFT. I then go on to present several investigations centering around the framework of dualities between gauge theory and gravity systems. In chapters 2, 3, and 4 we consider several 10D solutions. Chapter 2 deals with the inclusion of D7 branes in a D3 brane background, which amounts to adding fundamental matter in the gauge theory dual. We consider including the gravitational backreaction of the D7 branes in these solutions. In chapter 3, we consider modifications to the 6D space transverse to a stack of D3 branes. The 6D spaces that we consider are cones over the so called <italic>Y<super> p,q</super></italic> geometries. We consider a geometric deformation for each of these spaces which explicitly breaks a <italic>U</italic>(1) isometry. In chapter 4, the leading Regge behavior string states are examined. We calculate the effective coupling of such string states to the five form and metric in a flat space background, and obtain an effective Lagrangian. Using this Lagrangian, we examine the energy, spin and angular momentum of these states in the AdS₅ x <italic>S</italic>5 background which is then compared to the semiclassical analysis of the literature. In chapters 5 and 6, we turn to discussions of the AdS₅ factor. The Karch Randall scenario, a brane world scenario based oil AdS₄ slices of AdS₅ naturally suggests considering transparent boundary conditions for the field theory in AdS₄. In chapter 5 we show that with these boundary conditions, a mass is induced for the graviphoton, and that this mass is in the correct proportion to the graviton mass (studied in the literature) to preserve supersymmetry. In chapter 6 we examine black hole solutions in AdS₅. The presence of the black hole breaks some of the global supersymmetries (present in pure AdS₅) which we use to generate the superpartners to these black holes. Using boundary counter term techniques, we find the mass, angular momentum, and charge of these superpartners and use this to determine the representation of the AdS₅ superalgebra that these black holes belong to. In chapter 7 and 8 we turn to the field theory side of AdS/CFT. Here, we consider certain discrete symmetries of these field theories. The discrete symmetries are dual to the number operators for certain wrapped branes. We find that the generators for these discrete symmetries do not commute. This feature of wrapped branes was uncovered in the literature for the field theory dual to S5/<blkbd>Z3</blkbd> . In addition to generalizing this to certain classes of <italic> Y<super>p,q</super></italic> geometries in chapter 7, we also find that the non conformal case admits a centrally extended Heisenberg group structure in chapter 8.