Overview

In this dissertation we study several topics in string theory and quantum field theory, which we collect into three main parts. The first part contains some studies in the context of twistor string theory. Witten proposed that the perturbative expansion of N = 4 super Yang-Mills theory has a dual formulation in terms of a topological string theory on the supertwistor space CP3&vbm0;4 . We discuss extensions of this construction in two directions. First, we make some preliminary considerations on the possibility of having a similar twistor approach to perturbative gravity. Then we extend the construction to theories with lower supersymmetry by taking orbifolds in the fermionic directions of CP3&vbm0;4 . We consider N = 1 and N = 2 superconformal quiver gauge theories as specific examples. In the second part of the dissertation we study worldline methods in curved space. In particular, we use the N = 2 spinning particle to describe antisymmetric tensors of arbitrary rank propagating in a curved background. The path integral quantization of the N = 2 particle produces a novel and compact representation of the one loop effective action for generic differential p-forms, including the vector field as a special example. We study both the massless and massive case, and show that the worldline representation of the one loop effective action can be used to efficiently study various quantum effects for antisymmetric tensor fields of arbitrary rank in arbitrary dimension. In the last and final part we study some topics in the context of the AdS/CFT correspondence. We start by investigating the recently discovered description of half-BPS supergravity backgrounds in terms of one-dimensional free fermions. We study a generalization of this construction obtained by considering free fermions at non-zero temperature. The ADM mass of the corresponding supergravity background is shown to agree with the fermion thermal energy, and we propose a way to qualitatively match the entropy in the two sides. We then move on to study some aspects of Wilson loops in AdS/CFT. In particular we focus on a newly discovered holographic dictionary relating Wilson loops in higher representations of the gauge group to D-branes in the bulk. We test the dictionary by computing correlators between chiral primary operators and half-BPS circular Wilson loops in higher representations, and find perfect agreement between the D-brane calculation and a matrix model result in the gauge theory side. We then consider extensions to Wilson loops with lower supersymmetries, and find two new D3 brane solutions dual to Wilson loops preserving 1/4 of the supersymmetries. Finally, we present a large new family of supersymmetric Wilson loops corresponding to arbitrary curves on the 3-sphere. These operators have in general non-trivial expectation value and preserve from 1/16 to 1/2 of the supersymmetries.

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