Aspects of branes in string theory

This thesis is devoted to the study of several aspects of branes in String/M theory. When an M-theory fivebrane wraps a holomorphic four-cycle P in a Calabi-Yau three-fold X the low energy dynamics is that of a black string in five-dimensional N = 1 supergravity. The infrared dynamics on the string worldsheet is an N = (0,4) 2D conformal field theory. Assuming the 2D CFT can be described as a nonlinear sigma model, we describe the target space geometry of this model in terms of the data of X and P . Variations of weight-two Hodge structures enter the construction of the model in an interesting way. A natural extension is the study of M-theory fivebranes wrapped on Special Lagrangian submanifolds (Sigma n) in Calabi-Yau four-folds. When the M5 wraps a four-cycle, the resulting theory is a two-dimensional domain wall embedded in three-dimensional bulk with at least two supercharges. We derive the theory on the wall in terms of the geometry of the Calabi-Yau manifold and the cycle Sigma4. As an example of the use of D-branes in field theory, we show how Nahm's equations and boundary conditions arise naturally in the context of D-brane physics by considering a system in type IIB string theory of N infinite parallel D1-branes perpendicular to a D3-brane. In the context of supergravity solutions corresponding to brane configurations, we examine the problem of finding the geometry corresponding to a D3-brane wrapping the three-cycle of the deformed conifold. We reformulate the problem in a way that can in principle provide an explicit solution. We derive an explicit metric for the deformed conifold using the machinery of coset spaces. As an example of brane-world scenarios, we consider deformations of singular "dilatonic global cosmic string" compactifications. The deformations are obtained by allowing a constant curvature metric on the brane and they correspond to a choice of integration constant. We show that there exists a unique value of the integration constant that gives rise to a nonsingular solution. The metric on the brane is dS4 with an exponentially small value of expansion parameter. We derive an upper bound on the brane cosmological constant. We give an embedding of these solutions to type IIB supergravity.