Studies in gauge/string dualities

Dualities are among the most powerful tools in theoretical physics and, particularly, in string theory. The ones relating gauge field theories and theories of strings, the gauge/string dualities, are specially important and constitute the focus of this dissertation. We consider several topics in the context of two such dualities, the AdS/CFT correspondence and twistor string theory. In the part about the AdS/CFT correspondence we start by studying the thermodynamics of type IIB superstrings on the maximally supersymmetric plane wave background, computing in particular the Hagedorn temperature of non-interacting strings and analyzing the limits of small and large background Ramond-Ramond flux. We then consider a half-BPS supergravity solution whose moduli space can be mapped to the phase space of a gas of free fermions in a harmonic potential at finite temperature. We can match the ADM mass of the geometry with the thermal energy of the fermions and propose a way to also match the entropies in the two pictures. The last chapter of this part is dedicated to the study of supersymmetric Wilson loops. We first introduce a large new family of loop operators preserving various amounts of supersymmetry, from two to sixteen supercharges. We then study a novel description of higher rank loops in terms of electrically charged D-branes. In particular, we compute correlation functions between such loops and chiral primary operators of N = 4 super Yang-Mills theory and present the D-brane solutions corresponding to some examples of quarter-BPS loop operators. In the part about twistor string theory we first extend the conjectured equivalence between perturbative N = 4 super Yang-Mills and the topological B-model on CP3|4 to N = 1 and N = 2 superconformal quiver gauge theories. This is achieved by orbifolding the fermionic directions of the supertwistor space. We also consider some explicit quivers and compute several scattering amplitudes. Finally, we check the localization properties of some gravity amplitudes in twistor space and propose an extension of the twistor inspired MHV decomposition of Feynamn diagrams to the computation of tree level graviton scattering.